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\begin{document}
	
	\begin{frontmatter}
		
		\title{How to empower commercial satellite supply chain: Insurance, government subsidy or blockchain adoption?}
		
		\author[SEMUCAS]{Jichang Dong}\ead{jcdonglc@ucas.ac.cn}
		\author[SEMUCAS,SDCUCAS,BDCAS]{Yihan Jing}\ead{jingyihan18@mails.ucas.ac.cn}
		\author[SEMUCAS,BDCAS,MOECAS]{Zhou He\corref{Cor}}\ead{hezhou@ucas.ac.cn}	
		\author[ZNU]{Ciwei Dong}\ead{ dongciwei@zuel.edu.cn}		
  
    	\address[SEMUCAS]{School of Economics and Management, University of Chinese Academy of Sciences, 3 Zhongguancun Nanyitiao, China}
    	\address[SDCUCAS]{Sino-Danish College, University of Chinese Academy of Sciences, 80 Zhongguancun East Road, Beijing 100190, China.}    	
		\address[BDCAS]{Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, 80 Zhongguancun East Road, Beijing 100190, China.}
		\address[MOECAS]{MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS, 3 Zhongguancun Nanyitiao, China}
		\address[ZNU]{School of Business Administration, Zhongnan University of Economics and Law, Wuhan 430073, China}
		\cortext[Cor]{Corresponding author. Tel.: +86 10 88250000; fax: +86 10 88250000.}
			
	\begin{abstract}
	    The commercial satellite industry is booming with possible launch failures, which can cause enormous loss for both vehicle manufacturer and satellite operator.
	    To hedge such risks and reduce potential costs, they often buy launch insurance from financial companies, and/or seek possible subsidy from government-backed schemes.
	    Recently, the innovative blockchain technology has been adopted by satellite launch supply chains to enhance data sharing, improve workflow efficiency, and thus reduce launch risks.
	    However, very little research has been done on how these players interact, make decisions, and how the satellite supply chain (SSC) can be empowered by insurance, government subsidy or blockchain adoption.
		In this paper, we propose several Stackelberg games to examine the SSC cases with launch insurance (Model I), with insurance \& government subsidies (Model IG), with blockchain-embedded insurance (Model B), and with blockchain-embedded insurance \& government subsidies (Model BG).
		We investigate the optimal launch price, retail price, and the effort (for improving launch success probability) expressions by deriving models.
	    Furthermore, we explore the conditions for optimal allocation of government subsidies and the cost thresholds for adopting blockchain technology by analyzing the equilibrium outcomes.
	    We find that if the government wants to form a virtuous circle and optimize the allocation of funds, it should subsidize satellite operators that use cost-effective vehicles for launch activities rather than providing unconditional subsidies.
	    In addition, we also find that the subsidy does not benefit consumers, but blockchain can.
	    Once the blockchain technology is adopted, contract prices go up, the vehicle manufacturer exerts more effort, and the premium rate always is lower as the launch missions become more efficient and believable. 
	    Besides, the adoption of blockchain technology can also improve the benefits from government subsidies.
	    Moreover, when the satellite operator chooses an inexpensive launch vehicle, the cost-advantage blockchain-embedded platform benefits all participants. 
	    Finally, coupling these findings, we further discuss the managerial implications for the commercial space launch market.
		
	\end{abstract}
	
	\begin{keyword}
	 Satellite launch \sep insurance\sep government subsidy \sep blockchain \sep commercial launch supply chain
	\end{keyword}
	
%		\section{Highlights}
% 	(1) This paper investigates the implement of blockchain technologies in the commercial launch industry, which can effectively improve the efficient of data flow.\par 
%     (2)Two mathematical models have been built: insurance model and blockchain-embedded model.  \par 
%	(3) Uncover the threshold of using blockchain for each participant.\par 
%	(4) Reveal the adoption of blockchain can improve supply chain members to achieve a win-win situation. \par 
	
	\end{frontmatter}

	% usually, add a new page before introduction
	\newpage
	
	\section{Introduction}\label{sec:introduction}
	\subsection{Background}
	Man-made satellites can collect extensive and valuable data which can be used in archaeology, cartography, environmental monitoring, meteorology, and reconnaissance applications.
	Space is no longer confined to government and military agencies like NASA, but open to private companies since 1980s, thanks to the changes of space laws and regulatory regime \citep{OECD2014}.
	On Dec.3th 2013, the SES-8 satellite was successfully delivered by a Falcon 9 launch vehicle made by SpaceX, a private company founded in 2002 offering lower cost launches than their competitors \citep{spacex}.
	This successful launch significantly promotes the global satellite industry, the total revenue of which reaches \$386 billion by 2021 \citep{Space2022}.
	The commercial satellite industry put a record 1,713 commercial satellites into orbit for the fourth consecutive year, an increase of more than 40\% compared to 2020.
	
	Behind such vigorous development, the launch failure risk can not ignored by the companies in satellite launch supply chain (SSC).
	Once the launch fails, the loss for both vehicle manufacturer and satellite operator is enormous.
	To hedge this risk, there are three solutions in practice.
	
	First, space insurance emerged. 
	Insurance companies like \textit{Global Aerospace} have been providing different space insurance services, which can be roughly divided into four types according to satellite project phases: pre-launch insurance\footnote{	Pre-launch insurance covers damage to a satellite or launch vehicle during the construction, transportation, and processing phases prior to launch.}, launch insurance\footnote{Launch insurance covers losses of a satellite occurring during the launch phase of a project. It insures against complete launch failures as well as the failure of a launch vehicle to place a satellite in the proper orbit.}, in-orbit insurance\footnote{In-orbit policies insure satellites for in-orbit technical problems and damages once a satellite has been placed by a launch vehicle in its proper orbit.}, and launch plus life insurance\footnote{Third-party liability and government property insurances protect launch service providers and their customers in the event of public injury or government property damage, respectively, caused by launch or mission failure.}.	
    Among them, the launch insurance is most popular because the launch phase is the riskiest activity and the damage is often catastrophic \citep{Suchodolski2018, Gould2000, Kunstadter2020}.
    With more and more satellite operators realizing the importance of launch insurance, nearly half of satellite launches are insured \citep{Hussain2021}.
    
    Second, the government subsidized.
    Since the commercial industry promotes the development of high technologies, some governments have introduced policies to subsidize the SSC. 
    For example, the \textit{Beijing Bureau of Economy and Information Technology} subsidized commercial space enterprises that engage in the production and manufacture of vehicles and satellites, and encouraged them to establish headquarters, sales and operation in Beijing.
    In addition, the Unites States not only provided subsidy for launch liability insurance but also awarded the commercial companies directly.

    Third, new technology helped.
    Blockchain, a disruptive technology that facilitates data sharing and trust building, has been adopted by the SSC companies, such as \textit{SpaceChain}, \textit{IBM} and \textit{Cloud Constellation Corporation}. 
    It is used to share the critical data (e.g., contracts, test results) among trusted parties to make the workflow (e.g., approvals, auditing) more efficient and visible, so that the launch failure risk can be reduced as much as possible \citep{Zheng2021}.
    
    Each solution above introduces new entity (insurance company, government, and blockchain service provider) with different interest into the SSC.
	Hence, both the private companies and government are keen to understand the impacts of different solutions on SSC performance.
	
	\subsection{Research questions and key findings}
	This paper aims to study the following research questions (RQ):
	
	RQ1. How to analytically model the interactions among key entities in SSC, namely vehicle manufacturer (VM), satellite operator (SO) and insurance company (IC)? What is the optimal decision for each entity?
	
	RQ2. How to analyze the impact of government subsidy on the optimal decisions in SSC?
	
	RQ3. Is blockchain worth adopting to the SSC? How to understand its impacts on the optimal decisions?
	
	To investigate RQ1, we propose a benchmark model with three entities, called Model I.
	This model is extended as Model IG to study RQ2 by considering government subsidy.
	Next, the blockchain technology is introduced into both models as Model B and BG.
	Comparing the optimal decisions in these four models, we obtain the following results:

	\begin{enumerate} [(1)]
		\item Government subsidies can be used to incentivize SO to pay higher launch prices, so that the VM have the motivation to increase the probability of successful launches, and the overall social welfare (total profit of all players) also increases.
		\item The impacts caused by blockchain technology and government subsidy are similar; the difference is threefold: for SO, blockchain adoption (if the cost is low) increases its data retail price and profit; for VM, its profit depends on the cost of blockchain adoption and vehicle manufacturing; for satellite data customer, its surplus increases.
%		\item @@@ try to add another finding/result. No insurance-related results?
	\end{enumerate}

%	@@@carefully enumerate your contributions
	\subsection{Contributions}
	Th contributions of this paper are summarized as follows:
	(1) Inspired by the study on satellite industry operation management by \cite{Wooten2018}, we investigate SSC in a manner of game theory to study how financial factors, government support and technology advance affect the operations of SSC entities.
	(2) Different from the well-known supply chain financial models such as the one proposed by \cite{Tang2018}, we also consider the role of government subsidies, as well as disruptive FinTechs such as blockchain. 
	(3) Different from the existing blockchain-related supply chain studies, our model is one of the first attempts to investigate the SSC by combining real-world practices in satellite industry \citep{Altaf2019} and recent blockchain applications \citep{Luo2022}.
	%	(4) In terms of modeling, we have innovatively constructed a three-stage Stackelberg game model which characterizes the high-risk, high-loss nature of SSC.
	Therefore, we suggest that this paper not only complements the literature, but also provides managerial insights for practitioners in satellite industry.\par 
	
	The rest of this paper is organized as follows.
	\refsec{sec:review} reviews four related research streams.
	\refsec{sec:models} establishes the benchmark case with launch insurance (Model I), and introduces government subsidies into an extended case (Model IG).
	\refsec{sec:blockchain} examines the impact of blockchain adoption in the SSC under two scenarios, one with launch insurance (Model B) and one with government-subsidized launch insurance (Model GB).
	\refsec{sec:extensions} relaxes some assumptions to generate new findings.
	\refsec{sec:conclusions} concludes this paper and suggests potential topics for future research.

	
\section{Literature review}\label{sec:review}
	Our paper is closely related to four research streams: supply chain insurance, space supply chain management, blockchain, and government subsidies.
	
	\subsection{Supply chain insurance}
	Supply chain insurance is a sub-stream of supply chain finance which is extensively studied in today's FinTech era \citep{Zhao2015,Xu2018,Wang2021b}.
	Among the many types of commercial insurance, the one most similar to the space launch insurance in this paper is business interruption insurance (BI insurance). 
	In management practice, companies can utilize BI insurance to hedge against risks. 
	However, it must be pointed out that the purchase cost of BI insurance is high, and it is at the cost of sacrificing current profits to achieve risk aversion.
	If no interruption occurs during the insurance period, this premium will become a sunk cost for the enterprise.
	At this point, facing the high cost of current payment and the small probability of large economic losses in the future, the trade-off between risks and benefits becomes an important issue to be studied and solved in theory and practice.
	
	According to the different sources of risk, BI insurance can be divided into two categories: risk of endogenous disruption which mainly comes from within the supply chain (e.g., inventory shortages, cooperator's bankruptcy, transportation delays); and risk of exogenous disruption which Mainly from the external environment of the supply chain (e.g., Natural disaster risk, social risk and economic risk)  \citep{Sodhi2012a, Heckmann2015}.
	
	(1) Hedging endogenous risks.
	 \citet{Lin2010} compared insurance contract with revenue sharing contract according to different agents' risk aversion based on the news-vendor model.	
	 With the presence of inventory risk, \cite{Dong2012} applied BI insurance to a single-period product-inventory operation management.
	 Based on \cite{Dong2012}, \cite{Dong2018} considered the preparation strategy. By examining a two-stage model, the effects of inventory, preparedness, and BI insurance on the product chain are comparatively analyzed.
	 In the after-sales service context, \cite{Qin2020} constructed a principal-agent model by combining the insurance options with  after-sales service contracts to reduce operational risk (e.g., machine failure). Specifically, they consider two main forms of contracts: resource-based contract and performance-based contract.
	Besides, \citet{Wang2021} also discussed which contract is better for supply chain partners between the advanced payment contract, penalty contract, and time insurance contract in the express delivery supply chain. 
	(2) Hedging exogenous risk.
	\cite{LodreeJr2008} designed an insurance policy framework to quantify the risks and benefits. 
	\cite{Balcik2019} proposed a cooperative pre-deployment strategy between countries responding to hurricane disasters. The authors determined the location and quantity of relief supplies to be stored based on a stochastic programming model and developed a dataset for the network with real-world data.
	\cite{Yu2021} considered the interrupt probability of the supply chain, and illustrate that business interruption insurance increases the profit of each participant.
	\cite{Brusset2018} constructed a weather index, so that entrepreneurial risk can be transferred to other risk-takers through insurance or options contracts. 

	%Similar to these researches, our paper also adopts the insurance contract to hedge the interrupt risk while the focal point is in the space launch supply chain, which is remarkable for technical complexity, high quality \& reliability requirements, and colossal failure losses.
	%However, we also combine the blockchain technology with supply chain management which is timely and important.  


%	\subsection{Space supply chain management}
%	
%	There is a large body of literature dealing with the supply chain.
%	However, only a few of them applies to the space industry.
%	According to the available literature, the development of space supply chain is broadly divided into two phases.
%	
%	(1) Around 1950's, scholars began to pay attention to the space logistics which mainly serving the supply and re-supply during the space exploration.
%	\cite{Braun1954} mentioned the the necessity of space logistics in the Mars project and he also pointed out that the logistics support, which is a main contributor to success or failure, is an important part of the project.
%	\cite{Follett1965} gave the definition of the space logistics as a transportation of person and material from earth to outer places in space which involving the supply and re-supply of the exploration, and the maintenance of vehicles and bases.
%	During this stage, the main used logistics supply models are Backpack Model and Scheduled Re-supply Model.
%	To meet the requirements of the feasibility, reliability, affordability and maintenance of space explorations, \cite{Antol1999} combined the advantages of the above two models and proposed the establishment of the  International Space Station as a free flyer servicing node.
%	\cite{Cuplin2000} investigated the ability of satellite serving to do on-orbit considering the design objectives of "better, faster, cheaper".
%	\cite{Gavish2004} Scholars exploit a Markov decision model solved by dynamic programming methods to find the optimal policy for satellite launches, thus achieving cost savings for Low-earth orbit satellite system operators.
%	
%    (2) Until 2006, the concept of space supply chain \cite{Fayez2006} was put forward, marking a new stage in the researching development. 
%    In this stage, scholars not only considered the materials delivering narrowly, but also integrated the data, information, crew, knowledge and capital flow into the space supply chain \citep{Galluzzi2006}, which is more expansively.
%    Numerous academic conferences on the topic of space supply chain operations were held during that year, thus, 2006 was also called The Year of Space Logistics by The International Society of Logistics. 
%    In this stage, a number of research institutions represented by NASA, MIT and Jet Propulsion Laboratory have first conducted systematic and comprehensive research on space logistics which have been in the leading position in the world \citep{Cheng2009}.
%    To visually simulate the flow of space vehicles and supplies through the  interplanetary logistics network, MIT researchers developed the SpaceNet which is a simulation and optimization software \citep{Lee2008}.
%    Based on NASA project practices, \cite{Evans2006} discussed the  impact of traditional supply chain models on the efficiency of space supply chain operations, such as such as SCOR Model, Lean – Six Sigma, and Capability Maturity Model.
%    Besides, to optimize the transfer of supplies in space, \cite{Taylor2006} developed a heuristic optimization algorithm by extending the terrestrial logistics model and incorporate the astrodynamic relationships.
%    \cite{Brandimarte2013} constructed a MILP model subject to resource constraints. Specifically, the paper investigates the scheduling of different launchers and different mission profiles to schedule Low-earth orbit satellite.
%    \cite{Zhang2015} developed a multi-objective mixed integer planning model for the collaborative optimization of multi-center multi-satellite launch missions based on the nondominated sorting genetic algorithm II. In this paper, they focus on the optimization objectives of minimum launch cost and minimum launch failure probability to solve the collaborative programming problem for a large amount of satellite launch missions.
%    \cite{Chen2021} develops a flexibility management framework for space logistics mission planning under uncertainty through decision rules and multistage stochastic programming.
%    
%    In addition to articles focusing on operations research, the business issues in space supply chain operation are also worthy of study with the commercial space entities emerging \cite{Dewicki2010}.
%    Therefore, a number of scholars have recently conducted studies around operation management which are more relevant to our paper.
%    \cite{Tang2014} provided a framework to balance cost, time and risk in the aircraft supply chain.
%   	\cite{Wooten2018} examined the space industry's operation management, which involves manufacturing operations, supply chain management, and sustainable operations. Besides, they also outlined the challenges and essential questions related to stakeholders.
%   \cite{Raghunath2021} discussed the challenges that commercial space operation faces from a business perspective.
%   Furthermore, \cite{Guo2021} comprehensively analyzed the global aerospace industry's current situation and future development from the upstream supply chain, midstream production chain, and downstream application chain.
%   In addition, \cite{Donelli2021} considered the profitability and efficiency during the aircraft manufacturing and supply chain. The paper proposed a model-based approach to optimal the multiple-choice.

   
 
%	As review literature, most papers target SCM in space give the mathematical model from optimizing logistics, even the system flow. While our paper builds models from the business angle, we concentrate on the game theory between participants during the launch activity. 
	
	

	\subsection{Blockchain technology in supply chain management}
	As a “trust ledger”, blockchain has overwhelming advantage of data storage such as openness, transparency, tampering, and traceability, which make it possible to manipulate higher quality data \citep{Choi2019}, improving the supply chain efficiency and so on  \citep{Chod2020}. 
	According to its characters, \cite{Queiroz2019,Wang2019,Babich2020, Li2022} gave the review of this topic.\par 
	Besides, more and more scholars have begun to study the application of blockchain in the supply chain. 
	(1) Inside the supply chain, (i) in upriver of supply chain, blockchain technology facilitates the flow of raw materials from the suppliers \citep{ Naydenova2017, Nash2016}; 
	(ii) in the midstream, it promotes the exchange of manufacture information and design smart contracts between participants in the supply chain upstream and downstream and achieve coordination eventually \citep{Moise2018, Hilary2022, Chod2020,Korpela2017,Wang2021a}. 
	(2) Outside the supply chain, 
	(i) face the third party, it provides an innovative way for the capital constraint companies to finance \citep{Choi2020,Choi2021};
	(ii) face the market, it helps products to fight counterfeits, earn trust of customers and win company reputation in the market \citep{Pun2021, Shen2021,Fan2020}.\par 
	Regarding our topic, this article mainly refers to articles on the application of blockchain in the space supply chain.
	\cite{Luo2022} adopted blockchain technology to enhance systems security and examined its affection on the government’s penalty system.
	\cite{Adhikari2020} gave a clearly analysis on the implementation of blockchain in the area of space cybersecurity framework against global positioning system spoofing.
	\cite{Clark2020} developed a secure system by leveraging the distributed ledger technology of blockchain for satellite networks. This system achieves reduced latency when transmitting data across constellations and reduces the burden in terms of quality, power and cost for all users.
	\cite{Zheng2021} studied a three-tier space supply chain under the decision-making problem and investigated how blockchain technology optimizes decisions based on information sharing.
	Moreover, \cite{HylandWood2020} examined three potential blockchain properties applied in space: real-time communication during the interplanetary space operating and operations realm of the solar system.
	\cite{Li2021} developed a framework based on blockchain technology which consists of an application layer, a contract and consensus layer, a data layer and a network layer to management the information of rocket and satellite launch.
	
	%However, different from them, this article's focal point is on launching a service supply chain supported by fintech ( blockchain-embedded insurance) to facilitate launching risks and contract pricing. 
	
	\subsection{Government subsidies}
	
	
	Government interventions in supply chain management include legislation \citep{Gouda2016, Zhang2018}, penalties \citep{Xiao2018,Luo2022}, subsidies \citep{Guo2019,Xiao2020,Jung2020} and taxes \citep{Xu2018a,Chen2020}. 
	The stream of research closest to our work is exploring the adoption of government subsidies to promote industry growth or to support firms through difficult times.
	
	In order to improve the social welfare and the manufacturers' profits, different types of subsidy programs has been launched by governments, such as subsidies to consumers, manufacturers, or both \cite{Yu2018}. The authors of this article reveal the influencing factors that determine the optimal structure of government subsidy programs. They find that governments can develop subsidy programs involving multiple competing manufacturers to improve consumer welfare.
	However, the government subsidy system is not always effective. \cite{Hsu2019} find that the quality subsidy offered to the farmers quality subsidies provided to farmers may reduce not only the quality of dairy products, but also the profitability of companies.
	\cite{Berenguer2017} analyze the effectiveness of subsidies on a for-profit or a not-for profit firm in inducing consumption. Their study shows that the incentive to a not-for-profit counterpart is more stronger than to a for-profit firm to encourage consumption.
	Besides, \cite{Bai2021} investigate the design of trade-in subsidy programs by capturing the essence of the interaction between the government, the manufacturer, and consumers. They find that compared with a fixed-amount subsidy, a shared subsidy program in which government subsidies are proportional to manufacturer rebates is more effective in stimulating consumers to trade-in.
	
	%In the same vein as the above literature, we also explore the effectiveness of government subsidies in supply chain operations. 
	%However, the difference is that we focus on the commercial space supply chain to explore how subsidy systems can be implemented to leverage its value.
	
	
%	\subsection{Contributions of this paper}
%	
%	To sum, in this section we have reviewed three research streams, comparing to the literature from these topics, our paper's contributions are as follows:
%	(1) Inspired by the study on satellite industry operation management by \cite{Wooten2018}, we investigate SSC in a manner of game theory to study how financial factors, government support and technology advance affect the operations of SSC entities.
%	(2) Different from the well-known supply chain financial models such as the one proposed by \cite{Tang2018}, we also consider the role of government subsidies, as well as disruptive FinTechs such as blockchain. 
%	(3) Different from the existing blockchain-related supply chain studies, our model is one of the first attempts to investigate the SSC by combining real-world practices in satellite industry \citep{Altaf2019} and recent blockchain applications \citep{Luo2022}.
%%	(4) In terms of modeling, we have innovatively constructed a three-stage Stackelberg game model which characterizes the high-risk, high-loss nature of SSC.
%	Therefore, we suggest that this paper not only complements the literature, but also provides managerial insights for practitioners in satellite industry.\par 



\section{The case with insurance and government subsidy} \label{sec:models}
	To answer the first two RQs, the Model I is first presented to describe the common practice of a SSC which uses commercial insurance to hedge launch risk.
	Next, the Model I is extended to the Model G by introducing government subsidy, which @@@
	The optimal decisions of entities under two models are compared in this section.
	
\subsection{Model I: SSC with insurance}\label{sec:modeli}	
	Consider an engineer-to-order SSC consisting of one vehicle manufacturer (VM, he), one satellite operator (SO, she) and an insurance company (IC, it). 
	The interactions among them are illustrated in \reffig{fig:sequence}.
	\begin{figure}[H]
		\centering
		\includegraphics[width=1\linewidth]{sequences.pdf}
		\caption{Sequence of events of model I. SO: satellite operator; VM: vehicle manufacture; IC: insurance company.}
		\label{fig:sequence}
	\end{figure}

	First, as in practice, the SO designs a launch service contract with launch price $l$ and prepay ratio $\alpha$, i.e., pay the VM $\alpha l$ up front \citep{Andrews2011,Barschke2020}.
	Second, as the follower, the VM decides whether to accept the contract.
	Following \cite{Tang2018}, we scale the base launch success probability to 0.
	To increase the probability from 0 to $e$, where $e \in (0, 1)$, the VM needs to exert effort associated with a dis-utility $ke^2$ with $k > 0$.
	Third, the SO buys the launch insurance at the premium rate $r$ to compensate the loss if the launch fails.
	Hence, the VM receives the remaining payment $(1-\alpha)l$, if the launch is successful; or $0$, if the launch fails. 
	Finally, once the satellite works in orbit, the SO can sell the data to the market at the retail price $p$.
	Without loss generality, data customers possess a stochastic valuation $u$ towards the satellite data, which follows a distribution $f(u)$.
	Following most literature @@, we set $f(u)$ follows a uniform distribution, denoted by $U[0,1]$.
	To avoid facing messy mathematics, we normalize the consumer population as $1$, and thus the market demand $D^I$ is expressed as follows:	
	\begin{eqnarray}\label{eq:id}
		\begin{aligned}
			D^I &= 1 \int_{p}^{1}{f\left( u \right) \mathrm{d} u}= 1-p\\
		\end{aligned}
	\end{eqnarray}
		
	Model I is a Stackelberg game that can be solved using backward induction.	
	We summarize the notation used throughout the paper in \reftab{tab:Parameters}.
	\begin{table}[!htbp]
		\scriptsize
		\caption{\label{tab:Parameters} Notation}
		\centering
		\begin{threeparttable}
			\begin{tabular}{ll} % lcr: left, center, right
				\toprule
				Variable & Remark\\		
				\midrule
				Model I & Satellite launch supply chain with insurance\\
			    Model IG& Satellite launch supply chain with government-subsidized insurance \\
			    Model B & Blockchain-embedded satellite launch supply chain with insurance \\
			    Model BG & Blockchain-embedded satellite launch supply chain with government-subsidized insurance  \\
			    $p$ & The satellite data retail price \\
				$l$ & The launching service price \\	
		     	$\alpha$ & The upfront payment ratio \\
				$e$& The “rate of successful launch ”, which is the same as “the level of effort the VM exerting” in this paper \\	
			    $k$& The cost coefficient of effort\\			
				$r$ &The premium rate \\
				$\beta$& The claim ratio\\
				$g$& The government-subsidized launch insurance premium rates\\				
				$c_i$& The cost of vehicle $(i= V)$ or satellite $(i= S)$ \\
				$\theta$ & The penalty of a failed launch for VM\\
				$k$ & The effort cost factor\\		
				$\pi_i$ & The profit of vehicle manufacture$(i= V)$ or satellite operator $(i= S)$ or insurance company $(i=I)$\\
				$CS$& The consumer surplus\\
				$SW$& The social welfare\\	
				\bottomrule
			\end{tabular}
			\begin{tablenotes}
				\item[a] Subscripts $S$, $V$ and $I$ denote the indices of SO, VM and IC respectively.
				\item[b] Superscript $I$, $IG$, $B$ and $BG$ denote functions and decisions in model I, model IG, model B and model BG respectively. 
			\end{tablenotes}
		\end{threeparttable}
	\end{table}
	
	\subsubsection{The VM’s effort}
	From the perspective of VM, a launch failure results in not only the current contract loss but also the damage of his reputation and future business as well as financing. 
	To reflect the VM's additional loss, a penalty denoted by $\theta$ is adopted into his profit function $\piv$:
	\begin{eqnarray}\label{eq:vm:payoff}	
		\begin{aligned}
			\max_e \E [\piv(l, p, e)] &=\alpha l+ (1 - \alpha)el - (1 - e) \theta - (ke^2 + \cv),\\
			s.t.~\piv &\geq 0
		\end{aligned}
	\end{eqnarray}
	where $\cv$ denotes the rocket cost.
	$\piv$ can be divided into three parts: 
	(1) the prepaid income and expected gain upon successful launch $\alpha l+ (1 - \alpha)el$;
	(2) the expected loss of failure penalty in the event of launch failure $(1 - e) \theta$; and 
	(3) the cost of effort and vehicle $ke^2 + \cv$.
	
	The VM will reject the contract if the non-negative profit constraint is violated; otherwise, he decides the effort level $e$ to maximize his profit $\piv$.
	By zeroing the first-order condition of \refequ{eq:vm:payoff}, the VM’s best response (i.e., effort $e$) can be viewed as a function of launch price $l$: 
	\begin{eqnarray}\label{eq:ei} %\nonumber
		e(l)&=\frac{(1-\alpha)l+\theta}{2k},\\
		~s.t.&0<e\leq 1. \label{eq:ec}
	\end{eqnarray}\par

	By substituting \refequ{eq:ei} into the VM’s payoff $\piv$ given in \refequ{eq:vm:payoff}, it can be obtained that:
	\begin{eqnarray} 
		\piv=\frac{[(1-\alpha)l+\theta]^2}{4k}+\alpha l-\theta-\cv
	\end{eqnarray}\par

	Hence, considering the VM's non-negative profit constraint, i.e., $\piv \geq0$ , the lowest VM’s acceptance (VA) launch price can be written as:
	\begin{eqnarray}\label{eq:pv}
		 l \geq l_{VA} \equiv \frac{2\omega-2\alpha k-(1-\alpha) \theta}{(1-\alpha)^2},
	\end{eqnarray}
	where $\omega=\sqrt{(1-\alpha)^2 k \cv+ \alpha ^2 k^2 - (1-\alpha)k \theta}$.
    
	\subsubsection{The IC's premium rate}
	After observing the contract price $l$ selected by the SO, the insurance company can anticipate the VM’s effort $e(l)$ as given in \eqref{eq:ei}.
	Operating in a competitive market, the insurer sets its rate $r$ to its break-even point in expectation.
	In other words, under the rate $r$ that it offers, the insurance company’s expected payoff, $r (\cs + \alpha l)$, equals the amount of coverage, $ (1-e)(\cs + \alpha l)\beta$.
	Thus the IC's profit function can be written as:
	\begin{eqnarray}
		\begin{aligned}
		\pi_i^I &= (\cs + \alpha l) r - (1-e)(\cs + \alpha l) \beta, \label{eq:pii}\\
	   \end{aligned}
	\end{eqnarray}
	and its premium rate is also a function of $l$:
	\begin{eqnarray}
		\begin{aligned}
			r(l)& = \big[ 1-\frac{(1-\alpha)l+\theta}{2k} \big] \beta.\label{eq:ri}\\
		\end{aligned}
	\end{eqnarray}
 
	\subsubsection{The SO's optimal price}	
	From the perspective of SO, her payoff $\pis$ is a function of $l, p, e, r$ to be maximized by deciding two prices: the launch price $l$ and the data sale price $p$.
	In particular, her objective function is formulated as follows:
	\begin{eqnarray}\label{eq:iso:payoff}
		\begin{aligned}
			\max_{l,p} \E [\pis(l, p, e, r)] &= epD^I -[\alpha + (1-\alpha)e]l - (\cs + \alpha l)r + (1-e) (\cs + \alpha l) \beta- \cs,\\
		\end{aligned}
	\end{eqnarray}
	which consists of five parts:
	(1) the income of selling data once the satellite works in orbit $epD^I$;
	(2) the launch service price, i.e., $\alpha l + (1-\alpha)el + (1-e)\times 0 = [\alpha+(1-\alpha)e]l$;
	(3) the premium for the launch insurance $(\cs + \alpha l)r$; 
	(4) the compensate she will receive from IC once the launch fails, $(1-e)(\cs + \alpha l)\beta$, where the insurance is assumed to cover $\beta$ of the whole loss including the cost of satellite $\cs$ and the prepay price $\alpha l$;
	(5) the cost of building the satellite $\cs$.
	Without loss of generality, the data income covers its building and launch cost, i.e., the SO sets a contract only when $pD^I\geq \cs + l $.
	
	Anticipating the VM’s best response $e$ given in \eqref{eq:ei} and the premium rate \eqref{eq:ri}, the SO’s payoff given in \refequ{eq:iso:payoff} can be rewritten as:
	\begin{eqnarray}\label{eq:so:payoff_p}	
		\begin{aligned}
			  \max_p \E [ \pis (l, p)] &=\ds \frac{[pD^I-(1-\alpha)l] \times [(1-\alpha)l+\theta]}{2k} - \alpha l-\cs,\\
			 ~ l &\geq l_{VA}.\\
		\end{aligned}
	\end{eqnarray}
	
	Checking the Hessian matrix of SO's payoff, we find $\pis$ is concave in $l$ and $p$ jointly when $0 < k < \frac{(1-\alpha) (1+4\theta)}{8\alpha}$. 
	Hereafter, we assume that this in-equation always holds, then the optimal launch price and optimal retail price of the SO are
	\begin{eqnarray}\label{eq:so:ls}	
		\begin{aligned}
			l_{S}=\frac{\phi-8\theta(1-\alpha)}{8(1-\alpha)^2}
		\end{aligned}
	\end{eqnarray}
	and $p^*=\frac{1}{2}$, where $\phi=(1-\alpha)(1+4\theta)-8\alpha k$. 
	Consider the VM's non-negative profit constraint, the SO aims to select the optimal contract price $l^* = \max(l_S, l_{VA}) $ that maximizes her payoff $\pis$.
	The optimal contract and corresponding equilibrium outcomes are given in \reflem{lemma:modeli}, in which the consumer surplus and social welfare are defined as follows:
	\begin{eqnarray}
		\begin{aligned}
			{CS}^I &= 1 \int_{p}^{1}(u-p){f\left( u \right) \mathrm{d} u}=\frac{(D^I)^2}{2},\label{eq:CS}	\\
			{SW}^I &=\pis+\piv+CS^I. \\
		\end{aligned}
	\end{eqnarray}

	\begin{lem} \label{lemma:modeli}
		The equilibrium outcomes of Model I are shown in \reftab{tab:modeli_decisions}, in which $\phi=(1-\alpha)(1+4\theta)-8\alpha k$ to avoid complicated writing.
	\end{lem}

	\begin{table}[htbp]
		\scriptsize
		\caption{\label{tab:modeli_decisions} The equilibrium outcomes in Model I.}
		\centering
		\begin{tabular}{lcc}		
			\toprule
			& \multicolumn{1}{c}{$\cv < H(\alpha)$ (i.e., $l_S>l_{VA}$) } & \multicolumn{1}{c}{$\cv \geq H(\alpha)$ (i.e., $I_{VA} \geq l_S$ ) }  \\
	     	\midrule
			Effort of VM exerting $e^*$ & $\frac{\phi}{16(1-\alpha)k}$ & $\frac{\omega-\alpha k }{(1-\alpha)k}$  \\
			Launch price $l^*$ & $l^*=l_{S}=\frac{\phi-8\theta(1-\alpha)}{8(1-\alpha)^2}$ & $l^*=l_{VA}= \frac{2\omega-2\alpha k-(1-\alpha) \theta}{(1-\alpha)^2}$\\ 
			Retail price $p^*$ & $\frac{1}{2}$ & $\frac{1}{2}$\\
			Premium rate $r^*$ & $\beta(1-\frac{\phi}{16(1-\alpha)k})$ & $\beta\frac{k-\omega}{(1-\alpha)k}$\\
			SO's profit $\pis$ & $\frac{\phi^2}{128(1-\alpha)^2k}+\frac{\alpha \theta}{1-\alpha} -\cs$ & $\frac{(\omega-\alpha k)(\phi+8\alpha k-8\omega)}{4(1-\alpha )^2k}+\frac{\alpha \theta}{1-\alpha}-\cs$\\
			VM's profit $\piv$ & $\frac{\phi^2+32\alpha k\phi}{256(1-\alpha)^2k}-\frac{ \theta}{1-\alpha}-\cv$ & $0$\\
			Consumer surplus $CS^I$ & $\frac{1}{8}$ & $\frac{1}{8}$ \\
			Social welfare $SW^I$ & $\frac{3\phi^2+32\alpha k\phi}{256(1-\alpha)^2k}- \theta-\cs-\cv+\frac{1}{8}$ & $\frac{(\omega-\alpha k)(\phi+8\alpha k-8\omega)}{4(1-\alpha )^2k}+\frac{\alpha \theta}{1-\alpha}-\cs+\frac{1}{8}$\\
			\bottomrule			
		\end{tabular}
	\end{table}
	
	Because the launch price $l^* = \max(l_S, l_{VA})$ has two possible values, there are also two cases in our equilibrium result: $\cv<H(\alpha) $ and $\cv \geq H(\alpha)$, where $H(\alpha)=\frac{8(1-\alpha)[2\alpha k+\theta(1-\alpha)]+16\theta^2(1-\alpha)^2-192\alpha^2k^2-64\theta k(1-\alpha)(4-\alpha)}{256(1-\alpha)^2k}$.
	In the first case, the SO's optimal launch price $l_S$ is higher than $l_{VA}$, which yields that $\cv <H(\alpha)$ by merging \eqref{eq:pv} and \eqref{eq:so:ls}.
	In the second case, the SO's optimal launch price $l_S$ is lower than $l_{VA}$, then the contract price $l^*$ is $l_{VA}$ to prevent negative profit for the VM; otherwise the VM will quit the SSC.

	\subsubsection{Sensitivity analysis}
	According to the equilibrium outcomes, we now conduct the sensitivity analyses for Model I and summarized the outcomes in \reftab{tab:modeli_and_ig_sensitivity}.
	\begin{table}[htbp]
		\scriptsize
		\caption{\label{tab:modeli_and_ig_sensitivity} Sensitivity analyses for Model I and Model IG.}
		\centering
		\begin{tabular}{l*{10}{c}}		
			\toprule
			& {Model}&{Situation}&{$e^*$}&{$r^*$}&{$l^*$}&{$p^*$} &{$\pi_S$}&{$\pi_V$}&{Consumer surplus}&{Social welfare} \\
			\midrule
			$k \uparrow$ & 	
			Model I &{$\cv < H(\alpha)$ } & 	
			$\downarrow$&$\uparrow$&$\downarrow$&$-$&$\downarrow$ ($k<k_1)$&$\downarrow$&$-$&$\downarrow$\\
			&&&&&&&$\uparrow (k\geq k_1)$ &&&\\
			&&{$\cv \geq H(\alpha)$}
			&$\downarrow$&$\uparrow$&$\uparrow$&$-$&$\downarrow$&$-$&$-$&$\downarrow$\\
			\cline{2-11}
			&Model IG& {$\cv < H(\alpha)$ } &
			$\downarrow$&$\uparrow$&$\downarrow  (0<g<1)$&$-$&$\downarrow$ ($k<k_2)$&$\downarrow$&$-$&$\downarrow$\\
			&&&&&$-~(g=1)$&&$\uparrow (k\geq k_2)$ &&&\\
			&&{$\cv \geq H(\alpha)$ }&
			$\downarrow$&$\uparrow$&$\uparrow$&$-$ &&&&\\ 
			\hline
			$\theta \uparrow$&
			Model I &{$\cv < H(\alpha)$ } & 	
			$\uparrow$&$\downarrow$&$\downarrow$&$-$&$\uparrow$&$\uparrow (\theta<\theta_{V1})$&$-$&$\uparrow (\theta<\theta_{W1})$\\
			&&&&&&&&$\downarrow (\theta \geq \theta_{V1})$&&$\downarrow (\theta \geq \theta_{W1})$\\
			&&{$\cv \geq H(\alpha)$}&
			$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
			\cline{2-11}
			&Model IG& {$\cv < H(\alpha)$ } &
			$\uparrow$&$\downarrow$&$\downarrow$&$-$&$\uparrow$&$\uparrow (\theta<\theta_{V2})$&$-$&$\uparrow (\theta<\theta_{W2})$\\
			&&&&&&&&$\downarrow (\theta \geq \theta_{V2})$&&$\downarrow (\theta \geq \theta_{W2})$\\
			&&{$\cv \geq H(\alpha)$}&
			$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
			\hline
			$g \uparrow$&
			Model IG& {$\cv < H(\alpha)$ } & 
			$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$\uparrow$&$-$&$\uparrow$\\
			&&{$\cv \geq H(\alpha)$}&
			$-$&$-$&$-$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
			\bottomrule	
			\multicolumn{11}{l}{To avoid complicated writing, we define 
				$k_1= \frac{(1-\alpha)\theta}{2\alpha}$,
				$k_2=\frac{(1-\alpha)\theta}{2\alpha(1-g)}$,
				$\theta_{V1}=\frac{8k-2\alpha k}{1-\alpha}$, 
				$\theta_{V2}=\frac{8k-2\alpha k(1-g)}{1-\alpha}$,
				$\theta_{W1}=\frac{8k-6\alpha k}{3(1-\alpha)}$, $\theta_{W2}=\frac{8k-6\alpha k(1-g)}{3(1-\alpha)}$. }		
		\end{tabular}
	\end{table}
	
	First, we explore how the cost coefficient of effort $k$ affects the equilibrium outcomes mentioned above.
	If the cost coefficient of effort $k$ increases:
	\begin{itemize}
		\item Independent of the manufacturing cost of the vehicle $\cv$, the effort exerted by the VM $e$ and the launch price $l$ will always decrease, the premium rate $r$ will always increase, and the retail price $p$ is constant;
		\item Depending on $\cv$: when $\cv< H(\alpha)$ (i.e. $l^*=l_S$), the launch price $l$ will decrease; otherwise, it will increase. That is because the body who determines the launch price has changed. When $\cv<H(\alpha)$, it is the SO that decreases the contract price according to the decreasing effort $e$. But when $\cv \geq H(\alpha)$, the launch price equals the acceptance line which is determined by the VM, who will increase the contract price to compensate for the increasing effort cost.
		\item For the premium rate, the IC sets it according to the effort $e$, so it will increase with the decreasing successful launch probability.
		\item The VM's profit and social welfare always decrease.
		\item For the SO, in the situation $\cv<H(\alpha)$, her profit will increase when $k<k_1$, where $k_1= \frac{(1-\alpha)\theta}{2\alpha}$, otherwise $\pis$ will decrease when $k \geq k_1$.
	\end{itemize}

	Second, we examine how penalty cost $\theta$ affects these optimal outcomes.
	If the failed-launch penalty $\theta$ increases:
	\begin{itemize}
		\item Independent of the manufacturing cost of the vehicle $\cv$, the effort exerted by the VM $e$ and the launch price $l$ will always increase (the VM has to exert more effort to increase the successful launch probability to avoid the expensive failed-launch penalty $\theta$), the premium rate $r$ will always decrease, and the retail price $p$ is constant;
		\item Depending on $\cv$: when $\cv< H(\alpha)$ (i.e. $l^*=l_S$), the launch price $l$ will still decrease with larger $e$, because the price-maker, the SO, has no motivation to increase the launch price $l$; in contrast, when $\cv \geq H(\alpha)$, the launch price $l$ will increase, because the price-maker, the VM, has to increase the contract price to compensate for the increase of failed-launch penalty.
		\item For the premium rate, the IC sets it according to the effort $e$, so it will decrease with the increasing successful launch probability.
		\item The SO's profit always increases.
		\item For the VM and the society, in the situation $\cv<H(\alpha)$, their profits will increase when $\theta$ satisfies with $\theta<\theta_{V1}$ and $\theta<\theta_{W1}$, respectively, where $\theta_{V1}=\frac{8k-2\alpha k}{1-\alpha}$ and $\theta_{W1}=\frac{8k-6\alpha k}{3(1-\alpha)}$, otherwise they both will decrease; in the other situation $\cv \geq H(\alpha)$, $\pis$ and $SW$ will decreases.
	\end{itemize}
			
\subsection{Model IG: Satellite launch supply chain with government-subsidized insurance}
Based on the practice of SSC and the satellite industry, we build model IG the government entity, which aims to promote the development of SSC by proposing an insurance subsidy program.
The event sequence of model I is changed slightly: after the IC decides the premium rate $r$, the government will determine a subsidized rate $g$.
The interactions among the SSC entities are illustrated in \reffig{fig:sequence_g}, in which the only difference between model I and model IG is that the SO will obtain an insurance subsidy $g$.
\begin{figure}[H]
	\centering
	\includegraphics[width=1\linewidth]{sequences_g.pdf}
	\caption{Sequence of events of model IG. SO: satellite operator; VM: vehicle manufacture; IC: insurance company.}
	\label{fig:sequence_g}
\end{figure}

The market demand is given as follows:
\begin{eqnarray}\label{eq:igd}
	%	\left\{
	\begin{aligned}
		D^{IG} &= 1 \int_{p}^{1}{f\left( u \right) \mathrm{d} u}= 1-p\\
	\end{aligned}
	%	\right.
\end{eqnarray}

Then the payoffs of all entities can be measured as follows:
\begin{eqnarray}
	\begin{aligned}
		\pgs &= epD^{IG} -[\alpha + (1-\alpha)e]l - (r-g) (\cs + \alpha l) + (1-e)(\cs + \alpha l)\beta- \cs,\label{eq:igso:payoff}\\
		\pi_i^{IG}&= (\cs + \alpha l)r-(1-e)(\cs + \alpha l)\beta,\\
		\pgv&=[\alpha + (1 - \alpha)e]l - (1 - e) \theta - (ke^2 + \cv),\label{eq:igvm:payoff}\\
		s.t.~\pgv &\geq 0
	\end{aligned}
\end{eqnarray}

Following the similar derivation in \refsec{sec:modeli}, we obtain the equilibrium outcomes summarized in \reflem{lemma:modelig}.

\begin{lem} \label{lemma:modelig}
	The equilibrium outcomes of Model IG are shown in \reftab{tab:modelig_decisions}, in which $\psi=(1-\alpha)(1+4\theta)-8\alpha k(1-g)$ to avoid complicated writing.
\end{lem}

\begin{table}[htbp]
	\scriptsize
	\caption{\label{tab:modelig_decisions} The equilibrium outcomes in Model IG.}
	\centering
	\begin{tabular}{lcc}		
		\toprule
		& \multicolumn{1}{c}{$\cv < H(\alpha)$ } & \multicolumn{1}{c}{$\cv \geq H(\alpha)$ }  \\
		\midrule
		Effort of VM exerting $e^*$& 
		$\frac{\psi}{16(1-\alpha)k}$ & 
		$\frac{\omega-\alpha k }{(1-\alpha)k}$  \\
		Launch price $l^*$&
		$l^*=l_{S}=\frac{\psi-8\theta(1-\alpha)}{8(1-\alpha)^2}$&
		$ l^*=l_{VA}= \frac{2\omega-2\alpha k-(1-\alpha) \theta}{(1-\alpha)^2}$\\ 
		Retail price $p^*$&
		$\frac{1}{2}$&
		$\frac{1}{2}$\\
		Premium rate $r^*$&
		$\beta(1-\frac{\psi}{16(1-\alpha)k})$&
		$\beta\frac{k-\omega}{(1-\alpha)k}$\\
		SO's profit $\pgs$&
		$\frac{\psi^2}{128(1-\alpha)^2k}+\frac{(1-g)\alpha \theta}{1-\alpha} -(1-g)\cs$&
		$\frac{(\omega-\alpha k)(\psi+8\alpha k-8\omega)}{4(1-\alpha )^2k}+\frac{(1-g)\alpha \theta}{1-\alpha}-(1-g)\cs$\\
		VM's profit $\pgv$&
		$\frac{\psi^2+32\alpha k\psi}{256(1-\alpha)^2k}-\frac{ \theta}{1-\alpha}-\cv$&
		$0$\\
		Consumer surplus $CS^{IG}$&
		$\frac{1}{8}$&
		$\frac{1}{8}$\\
		Social welfare $SW^{IG}$&
		$\frac{3\psi^2+32\alpha k\psi}{256(1-\alpha)^2k}- \frac{\theta[1-(1-g)\alpha]}{1-\alpha}-(1-g)\cs-\cv+\frac{1}{8}$&
		$\frac{(\omega-\alpha k)(\psi+8\alpha k-8\omega)}{4(1-\alpha )^2k}+\frac{(1-g)\alpha \theta}{1-\alpha}-(1-g)\cs+\frac{1}{8}$\\
		\bottomrule			
	\end{tabular}
\end{table}

The optimal decisions of model IG are similar to that of model I, but there are three points worthy of notice.
\begin{itemize}
	\item When $\cv<H(\alpha)$, both the successful launch probability $e$ and launch price $l$ increase as each has a positive increment, as $\psi>\phi$. The premium rate $r$ will decrease due to government subsidy. 
	\item When $\cv\geq H(\alpha)$, the successful launch probability, launch price, and the premium rate are independent of the government subsidy. 
	\item The retail price remains unchanged, which means the government subsidy program doesn't affect the market retail price.
\end{itemize}

\subsubsection{Sensitivity analysis}
Regarding the sensitivity analysis, there are also three key findings.

First, if the cost coefficient of effort $k$ increases, 
(i) when $0<g<1$, the launch price $l$ will decrease in the first situation $\cv<H(\alpha)$; 
however, when $g=1$ the launch price will not be affected by $k$;
(ii) the threshold $k_2$ of SO's profit $\pgs$ to change direction is higher than $k_1$, where $k_2=\frac{(1-\alpha)\theta}{2\alpha(1-g)}$.

Second, if the launch-fail penalty $\theta$ increases, 
in the situation $\cv<H(\alpha)$, the thresholds of $\pgv$ and $SW^{IG}$, $\theta_{V2}$ and $\theta_{W2}$ are both higher than these of model I, where $\theta_{V2}=\frac{8k-2\alpha k(1-g)}{1-\alpha}$ and $\theta_{W2}=\frac{8k-6\alpha k(1-g)}{3(1-\alpha)}$. That means the VM and society can bear a higher penalty when the government launch the subsidy program.

Third, if the subsidy rate $g$ increases,
(i) when $\cv<h(\alpha)$, the successful launch probability $e$ and the launch price $l$ will increase, the premium rate $r$ will decrease; the SO's profit $\pgs$, the VM's profit $\pgv$ and social welfare $SW^{IG}$ will increase;
(ii)when $\cv \geq H(\alpha)$, all of the optimal decisions are not affected.
(iii) no matter in which situation, the consumer surplus do not change which means the government subsidy program can't benefit the customers.

\subsubsection{Values of government subsidies}\label{sec:value_g}
To further investigate the value of government subsidies, we define $V_{i}^{IG}$ as the equilibrium changes of indicator $i$ caused by government subsidies, where $i$ can be the successful launch probability, the premium rate, the launch price, the retail price, SO's profit, VM's profit, customer surplus, or the social welfare:
\begin{eqnarray}\label{eq:value_g}
	\begin{aligned}
		V_{x}^{IG}&=x^{IG}-x^I.\\
	\end{aligned}
\end{eqnarray}
We report the results in \reftab{tab:value_g}.
According to the sensitivity analysis, we obtain \refprop{prop:value_decision_g} and \refprop{prop:value_profit_g}.

\begin{table}[htbp]
	\scriptsize
	\caption{\label{tab:value_g} Values of government subsidies.}
	\centering
	\begin{tabular}{l*{9}{c}}		
		\toprule
		&{Case}&{$V_{ e^*}^{IG}$}&{$V_{ r^*}^{IG}$}&{$V_{ l^*}^{IG}$}&{$V_{ p^*}^{IG}$} &{$V_{SO}^{IG}$}&{$V_{VM}^{IG}$}&{$V_{CS}^{IG}$}&{$V_{SW}^{IG}$} \\
		\midrule
		 & 	
	    {$\cv < H(\alpha)$ } & 			   
		$\frac{8\alpha g}{16(1-\alpha)}$&$\frac{-8\beta\alpha g}{16(1-\alpha)}$&$\frac{\alpha g}{(1-\alpha)^2}$&$0$&
		$\frac{\psi ^2-\phi ^2}{128k(1-\alpha)^2}+\frac{g\alpha\theta}{1-\alpha}+g\cs$&$\frac{\psi ^2-\phi ^2+32\alpha k(\psi-\phi)}{256k(1-\alpha)^2}$&$0$&$	\frac{3(\psi ^2-\phi ^2)+256\alpha k g[\alpha k+(1-\alpha)\theta]}{256k(1-\alpha)^2}+g\cs$\\
		&{$\cv \geq H(\alpha)$ }&
		0&0&0&0&$g[\frac{(\omega-\alpha k)\alpha}{2(1-\alpha)^2}-\frac{\alpha\theta}{1-\alpha}+\cs]$&$0$&$0$&$g[\frac{(\omega-\alpha k)\alpha}{2(1-\alpha)^2}-\frac{\alpha\theta}{1-\alpha}+\cs]$\\
		\bottomrule			
	\end{tabular}
\end{table}


\begin{prop} \label{prop:value_decision_g}
	Given $\alpha,~ k,~ \theta,~g$, then $e^{IG}>e^I$, $r^{IG}<r^I$, $l^{IG}>l^I$ if and only if $\cv<H(\alpha)$.	
\end{prop}

\refprop{prop:value_decision_g} implies three findings when $\cv<H(\alpha)$.
First, given $k, \theta$, the launch insurance subsidy provided by the government can help to improve the successful launch probability $e$, and thus promote the development of satellite industry.
Second, the subsidy also helps to decrease the launch insurance rate $r$.
Since insurance rate is determined based on the break-even point of the IC, the larger the $e$, the smaller the $r$. 
Third, the launch price in model IG is also higher than that in model I, because SO is more willing to pay higher launch fees after receiving subsidies, and then the VM has the incentive to increase the probability of successful launches. 
However, the above findings do not hold when the SO chooses an expensive vehicle, i.e., $\cv>H(\alpha)$.

\begin{prop} \label{prop:value_profit_g}
	Given $\alpha,~ k,~\theta,~g$:
	\begin{enumerate}[(i)]
		\item  $\pgs>\pis$, $SW^{IG}>SW^I$.\par 
		\item  $\pgv>\piv$ if and only if $\cv<H(\alpha)$\par 
		\item  $CS^{IG}=CS^I$
	\end{enumerate}
\end{prop}
 
\refprop{prop:value_profit_g} also indicates three points.
First, given $k,~ \theta$, and $g$, the profit of SO and the social welfare in Model IG are always higher than those in Model I, i.e., they always benefit from the government's insurance subsidy program. 
Second, the profit of VM in Model IG is higher than that in Model I if and only if $\cv<H(\alpha)$.
The change of VM profit depends on the trade-off between higher effort cost and higher launch service income.
However, when the cost of the vehicle is relatively high, the VM cannot benefit from the government subsidy.
Third, the consumer surplus in Model IG equals that in Model I, implying that government subsidies have no impact on consumers.

To conclude, government subsidies help to improve the probability of successful launches, and to promote the formation of positive feedback in the commercial aviation industry.
However, this ``win-win'' outcome depends on the cost of vehicle: it must be relatively inexpensive, i.e., $\cv<H(\alpha)$.
Otherwise, if $\cv>H(\alpha)$, subsidies can only increase the profit of the SO, but the launch success rate can not be increased by government subsidies.

\section{The case with blockchain technology}\label{sec:blockchain}
Another approach to help hedge the launch risk is adopting disruptive technologies, such as the blockchain technology (BCT).
In practice, BCT affects the SSC in two ways.
On the one hand, it provides a decentralized identity management with strong security features, which engenders trust among SSC members (including customers) in the quality of the information being shared \citep{2020-Babich-p223-240}.
On the other hand, it improves the workflow efficiency of launch activities which helps to reduce the error rate, and thus increases the probability of successful launch.
In a blockchain-embed launch platform proposed by IBM, as depicted in \reffig{fig:blockchain}, BCT is able to deal with order tracking, parts assembly, shipments, and other workflows for approvals, auditing, launch and control in SSC, which will help the VM save cost and increase launch success probability.\par 
\begin{figure}[H] 
	\centering
	\includegraphics[width=0.7\linewidth]{blockchain}
	\caption{A blockchain-embed launch platform proposed by IBM, reproduced from source: \cite{Altaf2019}.} 
	\label{fig:blockchain}
\end{figure}

\subsection{Model B: Blockchain-embedded SSC with insurance}
Based on the above advantages of BCT, we assume that adopting BCT changes the origin model I in three ways (@@@ each add a citation):
\begin{itemize}
	\item For customers, the benefits brought by BCT are characterized by factor $b$ which will increase their utility. Hence the market demand can be written as follows:
	 \begin{eqnarray}\label{eq:igd}
		\begin{aligned}
			D^{B} &= 1 \int_{p-b}^{1}{f\left( u \right) \mathrm{d} u}= 1-p+b \\
		\end{aligned}
	\end{eqnarray}	
	\item For the VM, BCT decreases his effort cost exerting to improve the launch successfully probability from $k e^2$ to $k^B e^2$, where $0< k^B < k$.
	\item The BCT platform, provided by a third party, charges the SO and VM for $\csb$ and $\cvb$, respectively.
\end{itemize}
Therefore, the SSC members' payoffs can be measured as follows:
\begin{eqnarray}
	\begin{aligned}
		\pbs &= epD^B -[\alpha + (1-\alpha)e]l - (\cs + \alpha l)r + (1-e) (\cs + \alpha l) \beta - \cs-\csb,\label{eq:bso:payoff}\\
		\pi_i^{B}&= (\cs + \alpha l)r - (1-e) (\cs + \alpha l) \beta,\\
		\pbv&=[\alpha + (1 - \alpha)e]l - (1 - e) \theta - (\kb e^2 + \cv)-\cvb,\label{eq:bvm:payoff}\\
		s.t.~\pbv &\geq 0
	\end{aligned}
\end{eqnarray}
Using backward induction, we obtain \reflem{lemma:modelb}.
\begin{lem}\label{lemma:modelb}
	The equilibrium outcomes of Model B are shown in \reftab{tab:modelb_decisions}, where $\eta=(1-\alpha)(1+b)^2+4(1-\alpha)\theta-8\alpha \kb$, 
	$\mu=\sqrt{(1-\alpha)^2\kb (\cv+\cvb)+\alpha ^2{\kb}^2-(1-\alpha)\kb \theta}$.
\end{lem}

\begin{table}[htbp]
	\scriptsize
	\caption{\label{tab:modelb_decisions} The equilibrium outcomes in Model B.}
	\centering
	\begin{tabular}{lcc}		
		\toprule
		& \multicolumn{1}{c}{$\cv < H(\alpha)$ } & \multicolumn{1}{c}{$\cv \geq H(\alpha)$ }  \\
		\midrule
		Effort of VM exerting $e^*$& 
		$\frac{\eta }{16 (1-\alpha )\kb}$ & 
		$\frac{\mu-\alpha \kb }{(1-\alpha)\kb}$  \\
		Launch price $l^*$&
		$l^*=l_{S}=\frac{\eta-8\theta(1-\alpha)}{8(1-\alpha)^2}$&
		$ l^*=l_{VA}= \frac{2\mu-2\alpha \kb-(1-\alpha) \theta}{(1-\alpha)^2}$\\ 
		Retail price $p^*$&
		$\frac{1+b}{2}$&
		$\frac{1+b}{2}$\\
		Premium rate $r^*$&
		$\beta(1-\frac{\eta}{16(1-\alpha)\kb})$&
		$\beta\frac{\kb-\mu}{(1-\alpha)\kb}$\\
		SO's profit $\pbs$&
		$\frac{\eta^2}{128(1-\alpha)^2\kb}+\frac{\alpha \theta}{1-\alpha} -\cs-\csb$&
		$\frac{(\mu-\alpha \kb)(\eta+8\alpha \kb-8\mu)}{4(1-\alpha )^2\kb}+\frac{\alpha \theta}{1-\alpha}-\cs-\csb$\\
		VM's profit $\pbv$&
		$\frac{\eta^2+32\alpha \kb\eta}{256(1-\alpha)^2\kb}-\frac{ \theta}{1-\alpha}-\cv-\cvb$&
		$0$\\
		Consumer surplus $CS^B$&
		$\frac{(1+b)^2}{8}$&
		$\frac{(1+b)^2}{8}$\\
		Social welfare $SW^B$&
		$\frac{3\eta^2+32\alpha \kb\eta}{256(1-\alpha)^2\kb}- \theta-\cs-\cv-\csb-\cvb+\frac{(1+b)^2}{8}$&
		$\frac{(\mu-\alpha \kb)(\phi+8\alpha \kb-8\mu)}{4(1-\alpha )^2\kb}+\frac{\alpha \theta}{1-\alpha}-\cs-\csb+\frac{(1+b)^2}{8}$\\
		\bottomrule			
	\end{tabular}
\end{table}

The equilibrium outcomes in \reflem{lemma:modelb} are similar to \reflem{lemma:modeli}, but there are two notable differences.
First, when $\cv<H(\alpha)$, both the successful launch probability $e^*$ and launch price $l^*$ are higher than those in Model I; in contrast, the premium rate $r^*$ is lower than that in Model I. 
When $\cv\geq H(\alpha)$, the equilibrium outcomes of two models are compared in detail in \refsec{sec:value_b}.
Second, although the retail price $p^*$ is higher compared with Model I, the consumer surplus increases and only depends on $b$, no matter what the BCT cost is.
In other words, adopting BCT always improves the consumer surplus. 

\subsubsection{Sensitivity analysis}
We also obtain the sensitivity outcomes, reported in \reftab{tab:modeli_and_ig_sensitivity}.
\begin{table}[htbp]
 	\scriptsize
 	\caption{\label{tab:modeli_and_b_sensitivity} Sensitivity analyses for Model I and Model B.}
 	\centering
 	\begin{tabular}{*{11}{c}}		
 		\toprule
 		& {Model}&{Situation}&{$e^*$}&{$r^*$}&{$l^*$}&{$p^*$} &{$\pi_S$}&{$\pi_V$}&{$CS$}&{$SW$} \\
 		\midrule
 		$k \uparrow$ & 	
 		Model I &{$\cv < H(\alpha)$ } & 	
 		$\downarrow$&$\uparrow$&$\downarrow$&$-$&$\downarrow$ ($k<k_1$)&$\downarrow$&$-$&$\downarrow$\\
 		&&&&&&&$\uparrow$ ($k\geq k_1$) &&&\\
 		&&{$\cv \geq H(\alpha)$}
 		&$\downarrow$&$\uparrow$&$\uparrow$&$-$&$\downarrow$&$-$&$-$&$\downarrow$\\
 		\cline{2-11}
 		&Model B& {$\cv < H(\alpha)$ } &
 		$\downarrow$&$\uparrow$&$\downarrow $&$-$&$\downarrow$ $(k<k_3)$&$\downarrow$&$-$&$\downarrow$\\
 		&&&&&&&$\uparrow$ ($k\geq k_3$) &&&\\
 		&&{$\cv \geq H(\alpha)$ }&
 		$\downarrow$&$\uparrow$&$\uparrow$&$-$ &&&&\\ 
 		\hline
 		$\theta \uparrow$&
 		Model I &{$\cv < H(\alpha)$ } & 	
 		$\uparrow$&$\downarrow$&$\downarrow$&$-$&$\uparrow$&$\uparrow$ $(\theta<\theta_{V1})$&$-$&$\uparrow$ ($\theta<\theta_{W1}$)\\
 		&&&&&&&&$\downarrow$ ($\theta \geq \theta_{V1}$)&&$\downarrow$ ($\theta \geq \theta_{W1}$)\\
 		&&{$\cv \geq H(\alpha)$}&
 		$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
 		\cline{2-11}
 		&Model B& {$\cv < H(\alpha)$ } &
 		$\uparrow$&$\downarrow$&$\downarrow$&$-$&$\uparrow$&$\uparrow$ ($\theta<\theta_{V3}$)&$-$&$\uparrow$ ($\theta<\theta_{W3}$)\\
 		&&&&&&&&$\downarrow$ ($\theta \geq \theta_{V3}$)&&$\downarrow$ ($\theta \geq \theta_{W3}$)\\
 		&&{$\cv \geq H(\alpha)$}&
 		$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
 		\hline
 		$b \uparrow$&
 		Model B& {$\cv < H(\alpha)$ } & 
 		$\uparrow$&$\downarrow$&$\uparrow$&$\uparrow$&$\uparrow$&$\uparrow$&$\uparrow$&$\uparrow$\\
 		&&{$\cv \geq H(\alpha)$}&
 		$-$&$-$&$-$&$\uparrow$&$-$&$-$&$\uparrow$&$\uparrow$\\
 		\bottomrule		
 		\multicolumn{11}{l}{To avoid complicated writing, we define $k_1=\frac{(1-\alpha) \theta}{2\alpha}$, $k_3=\frac{(1-\alpha)[(1+b)^2+4\theta]}{8\alpha}$, $\theta_{V1}=\frac{8k-2\alpha k}{1-\alpha}$, $\theta_{V3}=\frac{32\kb-(1-\alpha)(1+b)^2-8\alpha \kb}{4(1-\alpha)}$,} \\
 		\multicolumn{11}{l}{$\theta_{W1}=\frac{8k-6\alpha k}{3(1-\alpha)}$, $\theta_{W3}=\frac{32\kb-3(1-\alpha)(1+b)^2-24\alpha \kb}{12(1-\alpha)}$}.
 	\end{tabular}
\end{table}
By comparing the sensitivity analysis results of Model B and Model I, we identify three differences.
First, if the effort cost coefficient increases, when $\cv<H(\alpha)$, there there exist a threshold $k_3=\frac{(1-\alpha)[(1+b)^2+4\theta]}{8\alpha}$ so that the SO's profit decreases as $k^B$ increases when $k^B<k_3$, otherwise $\pgs$ decreases.
Note that $k_3>k_2$, which means BCT raises this threshold of the SO and affects her profits.
Second, if the failed-launch penalty $\theta$ increases, when $\cv<H(\alpha)$, the VM's profit $\pi_V$ and social welfare $SW$ change with respect to $\theta_{V3}$ and $\theta_{W3}$ respectively, where $\theta_{V3}=\frac{32\kb-(1-\alpha)(1+b)^2-8\alpha \kb}{4(1-\alpha)}$ and $\theta_{W3}=\frac{32\kb-3(1-\alpha)(1+b)^2-24\alpha \kb}{12(1-\alpha)}$.
It is worth noting that the implementation of blockchain technology actually reduces the threshold of punishment to change the profit trend which means that the penalty tolerated by the VM and society is reduced, that is, once $\theta>\theta_{V3}$ and $\theta>\theta_{W3}$ both profits of them will decrease.
Third, if the benefits that blockchain brings to consumers $b$ increases, all equilibrium outcomes increase when $\cv<H(\alpha)$, except the premium rate $r^*$ that decreases.
When $\cv<H(\alpha)$, both the consumer surplus and social welfare increase, even the retail price increases as well.
Meanwhile, other indicators are not affected.

\subsubsection{Values of adopting BCT}\label{sec:value_b}
Similarly, we define the values of BCT by modeling $V_{x}^{B}$ as follows:
\begin{eqnarray}\label{eq:value_b}
	\begin{aligned}
		V_{x}^{B}&=x^{B}-x^I\\
	\end{aligned}
\end{eqnarray}

We report the results in \reftab{tab:value_decision_b} and \reftab{tab:value_profit_b}, then obtain \refprop{prop:value_decision_b} and \refprop{prop:value_profit_b}, which give the condition for adopting BCT.

\begin{table*}[htbp]
	\scriptsize
	\caption{\label{tab:value_decision_b} Values of BCT on optimal decisions.}
	\centering
	\begin{tabular}{ccccc}
		\toprule
		Situation & $V_{ e^*}^B$ & $V_{ r^*}^B$ & $V_{ l^*}^B$ & $V_{ p^*}^B$ \\
		\midrule 	
		$\cv < H(\alpha)$ & $\frac{k[(1+b)^2+4\theta]-\kb(1+4\theta)}{16k\kb}>0$ & $-\beta\frac{k[(1+b)^2+4\theta]-\kb(1+4\theta)}{16k\kb}<0$ & $\frac{(1-\alpha)(b^2+2b)+8\alpha(k-\kb)}{8(1-\alpha)^2}>0$ & $\frac{b}{2}>0$\\
		$\cv \geq H(\alpha)$ & $\frac{k\mu-\kb\omega}{k\kb(1-\alpha)}>0$ & $-\beta$$\frac{k\mu-\kb \omega}{k\kb(1-\alpha)}<0$ & $\frac{2(\mu-\omega)+2\alpha(k-\kb)}{(1-\alpha)^2}>0$ & $\frac{b}{2}>0$\\
		\bottomrule
	\end{tabular}
\end{table*}


\begin{table}[htbp]
	\scriptsize
	\caption{\label{tab:value_profit_b} Values of BCT on members' payoffs.}
	\centering
	\begin{tabular}{lllll}	
		\toprule
		Situation & $V_{ SO}^B$ & $V_{VM}^B$ & $V_{CS}^B$ & $V_{SW}^B$ \\
 		\midrule
		$\cv < H(\alpha)$ & $\frac{k\eta ^2-\kb \phi^2}{128k\kb (1-\alpha)^2}-\csb$ &
		$\frac{k\eta ^2-\kb \phi^2+32\alpha k \kb(\eta-\phi)}{256k\kb (1-\alpha)^2}-\cvb$&
		$\frac{b^2+2b}{8}$&
		$\frac{3k\eta ^2-3\kb \phi^2+32\alpha k \kb(\eta-\phi)}{256k\kb (1-\alpha)^2}+\frac{b^2+2b}{8}-\csb-\cvb$\\
		$\cv \geq H(\alpha)$ &
		$\frac{k(\mu-\alpha \kb)[\eta-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\phi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}-\csb$&
		$0$&
		$\frac{b^2+2b}{8}$&
		$\frac{k(\mu-\alpha \kb)[\eta-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\phi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}+\frac{b^2+2b}{8}-\csb$\\
		\bottomrule
	\end{tabular}
\end{table}

\begin{prop} \label{prop:value_decision_b}
	Given $\alpha$, $\kb$, $k$, $\theta$, $b$, then $e^{B}>e^I$, $r^{B}<r^I$, $l^{B}>l^I$, $p^{B}>p^I$.	
\end{prop}

\refprop{prop:value_decision_b} implies four points. 
First, the optimal effort exerted by the VM is higher after adopting BCT, which directly leads to a higher launch success probability. 
That also proves that BCT helps to improve work efficiency.
Second, the premium rate decreases as the successful launch probability increases.
Third, the launch price is higher with BCT, mainly because the probability of successful launch increases and the SO is willing to pay higher fees.
Fourth, the retail price in Model B increases after adopting BCT, as the BCT utility motivates customers to pay a higher retail price.

\begin{prop} \label{prop:value_profit_b}
		Given $\alpha$, $\kb$, $k$, $\theta$, $b$: 
	\begin{enumerate}[(i)]
		\item
		If $\csb ~ \big( \begin{smallmatrix} < \\ =\\> \end{smallmatrix}  \big)~ \min\{\frac{k\eta ^2-\kb \phi^2}{128k\kb (1-\alpha)^2},\frac{k(\mu-\alpha \kb)[\eta-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\phi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}\}$,
		then we have: $V_{ SO}^B~ \big(\begin{smallmatrix} > \\ =\\< \end{smallmatrix} \big) ~0$;
		\item
		When $\cv <H(\alpha)$, if $\cvb~ \big(\begin{smallmatrix} < \\ =\\> \end{smallmatrix} \big) ~\frac{k\eta ^2-\kb \phi^2+32\alpha k \kb(\eta-\phi)}{256k\kb (1-\alpha)^2} $ ,
		then we have: $V_{VM}^B~ \big(\begin{smallmatrix} > \\ =\\< \end{smallmatrix} \big) ~ 0$;
		when $\cv \geq H(\alpha)$, $V_{VM}^B \equiv 0$;
		\item
		$V_{CS}^B>0$;
		\item 
		When $\cv <H(\alpha)$, if $\csb+\cvb ~ \big( \begin{smallmatrix} < \\ =\\> \end{smallmatrix}  \big) \frac{3k\eta ^2-3\kb \phi^2+32\alpha k \kb(\eta-\phi)}{256k\kb (1-\alpha)^2}+\frac{b^2+2b}{8} $, then we have $V_{SW}^B ~ \big(\begin{smallmatrix} > \\ =\\< \end{smallmatrix} \big) ~ 0$;
		when $\cv \geq H(\alpha)$, if $\csb ~ \big(\begin{smallmatrix} < \\ =\\> \end{smallmatrix} \big) ~  \frac{k(\mu-\alpha \kb)[\eta-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\phi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}+\frac{b^2+2b}{8}$, then we have $V_{SW}^B ~ \big(\begin{smallmatrix} > \\ =\\< \end{smallmatrix} \big) ~ 0$.
	\end{enumerate}
\end{prop}

As shown above, \refprop{prop:value_profit_b} provides us four neat findings.

First, it computes the threshold of adopting BCT cost for the SO. 
When this cost is too high to be offset by extra retail revenue, launching through the BCT platform is not profitable.
Actually, there are two different thresholds for the SO to decide if the BCT should be adopted in two situations.
However, once BCT costs are pretty low, it is always profitable for the SO to use blockchain.

Second, it also yields the threshold and condition for the VM to adopt BCT.
When $\cv<H(\alpha)$ and the cost of BCT is low, the VM is able to make a profit. 
When $\cv$ is high, however, it is unprofitable for the VM to apply BCT ($V_{VM}^B \equiv 0$), as the launch price, offered by the SO, equals his acceptance level.

Third, the consumer surplus increases with the adoption of BCT, although they have to pay higher data retail prices.

Fourth, as shown in \refprop{prop:value_profit_b}, the social welfare will be improved with the adoption of BCT, as long as the cost of using BCT is lower than a specific threshold.

To conclude, the successful launch probability is always improved by the BCT in model BG, no matter if the SO chooses a cost-effective vehicle or not.
This is a significant difference compared with the impacts of government subsidies in \refprop{prop:value_decision_g}.
Besides, the BCT helps achieve an all-win situation for SSC members when the cost of BCT is relatively low. 
Therefore, the government may consider providing financial support for sponsoring BCT-embedded SSC to improve the successful launch rate and achieve an all-win situation.

\subsection{Model BG: Blockchain-embedded SSC with government-subsidized insurance}
In this section, we investigate the case when both government subsidies and BCT are applied in the SSC, which is represented by Model BG as follows:
\begin{eqnarray}
	\begin{aligned}
		\pbgs &= epD^{BG}-[\alpha + e(1-\alpha) ]l - r (\cs + \alpha l) + (1-e)\beta (\cs + \alpha l)- \cs-\csb,\\
		\pbgs&= (r-g) (\cs + \alpha l)-(1-e)\beta (\cs + \alpha l),\\
		\pbgv&=[\alpha + e (1 - \alpha) ]l - (1 - e) \theta - (\kb e^2 + \cv)-\cvb,\label{eq:bvm:payoff}\\
		s.t.~\pbv &\geq 0
	\end{aligned}
\end{eqnarray}

Again, we conduct backward induction and obtain \reflem{lemma:modelbg}.

\begin{lem} \label{lemma:modelbg}
	The equilibrium outcomes of Model BG are shown in \reftab{tab:modelbg_decisions}.
\end{lem}
\begin{table}[htbp]
	\scriptsize
	\caption{\label{tab:modelbg_decisions} The equilibrium outcomes in Model BG.}
	\centering
	\begin{tabular}{lcc}		
		\toprule
		& $\cv < H(\alpha)$ & $\cv \geq H(\alpha)$ \\
		\midrule
		Effort of VM exerting $e^*$& 
		$\frac{\lambda }{16 (1-\alpha )\kb}$ & 
		$\frac{\mu-\alpha \kb }{(1-\alpha)\kb}$  \\
		Launch price $l^*$&
		$l^*=l_{S}=\frac{\lambda-8\theta(1-\alpha)}{8(1-\alpha)^2}$&
		$ l^*=l_{VA}= \frac{2\mu-2\alpha \kb-(1-\alpha) \theta}{(1-\alpha)^2}$\\ 
		Retail price $p^*$&
		$\frac{1+b}{2}$&
		$\frac{1+b}{2}$\\
		Premium rate $r^*$&
		$\beta(1-\frac{\lambda}{16(1-\alpha)\kb})$&
		$\beta\frac{k-\mu}{(1-\alpha)\kb}$\\
		SO's profit $\pbgs$&
		$\frac{\lambda^2}{128(1-\alpha)^2\kb}+\frac{(1-g)\alpha \theta}{1-\alpha} -(1-g) \cs-\csb$&
		$\frac{(\mu-\alpha \kb)(\lambda+8\alpha \kb-8\mu)}{4(1-\alpha )^2\kb}+\frac{(1-g)\alpha \theta}{1-\alpha}-(1-g)\cs-\csb$\\
		VM's profit $\pbgv$&
		$\frac{\lambda^2+32\alpha \kb\lambda}{256(1-\alpha)^2\kb}-\frac{ \theta}{1-\alpha}-\cv-\cvb$&
		$0$\\
		Consumer surplus $CS^{BG}$&
		$\frac{(1+b)^2}{8}$&
		$\frac{(1+b)^2}{8}$\\
		Social welfare $SW^{BG}$&
		$\frac{3\lambda^2+32\alpha \kb\lambda}{256(1-\alpha)^2\kb}- \frac{\theta[1-(1-g)\alpha]}{1-\alpha}-(1-g)\cs-\cv-\csb-\cvb+\frac{(1+b)^2}{8}$&
		$\frac{(\mu-\alpha \kb)(\lambda+8\alpha \kb-8\mu)}{4(1-\alpha )^2\kb}+\frac{(1-g)\alpha \theta}{1-\alpha}-(1-g)\cs-\csb+\frac{(1+b)^2}{8}$\\
		\bottomrule		
		\multicolumn{3}{l}{To avoid complicated writing, we define $\lambda=(1-\alpha)(1+b)^2+4(1-\alpha)\theta-8\alpha \kb(1-g)$, $\mu=\sqrt{(1-\alpha)^2\kb( \cv+\cvb)+\alpha ^2{\kb}^2-(1-\alpha)\kb \theta}$.}
	\end{tabular}
\end{table}

Compared with the equilibrium outcomes in \reflem{lemma:modelig} (Model IG), the results of Model BG are different in two aspects:
First, the premium rate $r$ is lower than that in Model IG; while the successful launch probability $e$ and the launch price $l$ are higher, because $\kb$ is less than $k$ (smaller denominator) and $\lambda >\psi$ (larger numerator).
Second, although the retail price $p$ is higher than that in Model IG, the consumer surplus eventually increases due to a greater increase in market demand with the adoption of BCT. 

\subsubsection{Sensitivity analysis}
The sensitivity outcomes in model BG are reported in \reftab{tab:modelig_and_bg_sensitivity}.
\begin{table*}[htbp]
	\scriptsize
	\caption{\label{tab:modelig_and_bg_sensitivity} Sensitivity analyses for Model IG and Model BG.}
	\centering
	\begin{tabular}{*{11}{c}}		
		\toprule
		& {Model}&{Situation}&{$e^*$}&{$r^*$}&{$l^*$}&{$p^*$} &{$\pi_S$}&{$\pi_V$}&{$CS$}&{$SW$} \\
		\midrule
		$k \uparrow$ & 	
		Model IG &{$\cv < H(\alpha)$ } & 	
		$\downarrow$&$\uparrow$&$\downarrow$ ($0<g<1$)&$-$&$\downarrow$ ($k<k_2$)&$\downarrow$&$-$&$\downarrow$\\
		&&&&&$-$ ($g=1$)&&$\uparrow$ ($k\geq k_2$) &&&\\
		&&{$\cv \geq H(\alpha)$}
		&$\downarrow$&$\uparrow$&$\uparrow$&$-$&$\downarrow$&$-$&$-$&$\downarrow$\\
		\cline{2-11}
		&Model BG& {$\cv < H(\alpha)$ } &
		$\downarrow$&$\uparrow$&$\downarrow$ ($0<g<1$)&$-$&$\downarrow$ ($k<k_4$)&$\downarrow$&$-$&$\downarrow$\\
		&&&&&$-$ ($g=1$)&&$\uparrow$ ($k\geq k_4$) &&& \\
		&&{$\cv \geq H(\alpha)$ }&
		$\downarrow$&$\uparrow$&$\uparrow$&$-$ &&&&\\
		\hline
		$\theta \uparrow$&
		Model IG &{$\cv < H(\alpha)$ } & 	
		$\uparrow$&$\downarrow$&$\downarrow$&$-$&$\uparrow$&$\uparrow$ ($\theta<\theta_{V2}$)&$-$&$\uparrow$ ($\theta<\theta_{W2}$)\\
		&&&&&&&&$\downarrow$ ($\theta \geq \theta_{V2}$)&&$\downarrow$ ($\theta \geq \theta_{W2}$)\\
		&&{$\cv \geq H(\alpha)$}&
		$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
		\cline{2-11}
		&Model BG& {$\cv < H(\alpha)$ } &
		$\uparrow$&$\downarrow$&$\downarrow$&$-$&$\uparrow$&$\uparrow$ ($\theta<\theta_{V4}$)&$-$&$\uparrow$ ($\theta<\theta_{W4}$)\\
		&&&&&&&&$\downarrow$ ($\theta \geq \theta_{V4}$)&&$\downarrow$ ($\theta \geq \theta_{W4}$)\\
		&&{$\cv \geq H(\alpha)$}&
		$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
		\hline
		$b \uparrow$&
		Model BG& {$\cv < H(\alpha)$ } & 
		$\uparrow$&$\downarrow$&$\uparrow$&$\uparrow$&$\uparrow$&$\uparrow$&$\uparrow$&$\uparrow$\\
		&&{$\cv \geq H(\alpha)$}&
		$-$&$-$&$-$&$\uparrow$&$-$&$-$&$\uparrow$&$\uparrow$\\
		\hline
		$g \uparrow$
		& Model IG&  {$\cv < H(\alpha)$}
		&$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$\uparrow$&$-$&$\uparrow$\\
		&&  {$\cv >H(\alpha)$}
		&$-$&$-$&$-$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
		\cline{2-11}
		&Model BG&  {$\cv < H(\alpha)$}
		&$\uparrow$&$\downarrow$&$\uparrow$&$-$&$\uparrow$&$\uparrow$&$-$&$\uparrow$\\
		&&  {$\cv >H(\alpha)$}
		&$-$&$-$&$-$&$-$&$\uparrow$&$-$&$-$&$\uparrow$\\
		\bottomrule		
		\multicolumn{11}{l}{To avoid complicated writing, we define $k_2=\frac{(1-\alpha )\theta}{2(1-g)\alpha}$, $k_4=\frac{(1-\alpha)[(1+b)^2+4\theta]}{8(1-g)\alpha}$, $\theta_{V2}=\frac{8k-2(1-g)\alpha k}{1-\alpha}$, $\theta_{V4}=\frac{32\kb-(1-\alpha)(1+b)^2-8(1-g)\alpha \kb}{4(1-\alpha)}$, } \\
		\multicolumn{11}{l}{$\theta_{W2}=\frac{8k-6(1-g)\alpha k}{3(1-\alpha)}$, $\theta_{W4}=\frac{32\kb-3(1-\alpha)(1+b)^2-24(1-g)\alpha \kb}{12(1-\alpha)}$.}\\
	\end{tabular}
\end{table*}

Regarding the sensitivity analysis results, three differences between Model BG and Model IG are noted.
First, if the effort cost coefficient increases, when $\cv<H(\alpha)$, there there exist a threshold $k_4=\frac{(1-\alpha)[(1+b)^2+4\theta]}{8(1-g)\alpha}$ so that the SO's profit decreases as $k^B$ increases when $k^B<k_4$, otherwise $\pbgs$ increases.
Note that $k_3>k_2$, which means BCT raises the threshold of the SO and affects her profits.
Second, if the failed-launch penalty$\theta$ increase, when $\cv<H(\alpha)$, the VM's profit $\pi_V$ and social welfare $SW$ change with respect to $\theta_{V4}$ and $\theta_{W4}$ respectively, where $\theta_{V4}=\frac{32\kb-(1-\alpha)(1+b)^2-8(1-g)\alpha \kb}{4(1-\alpha)}$ and $\theta_{W4}=\frac{32\kb-3(1-\alpha)(1+b)^2-24(1-g)\alpha \kb}{12(1-\alpha)}$.
Similarly, once $\theta>\theta_{V4}$ and $\theta>\theta_{W4}$, both profits of them will decrease.
@@@

In addition, compared to \ref{tab:modeli_and_ig_sensitivity}, government subsidies also play a role and have the same effect on model IG and model BG.
(i) Firstly, in the case of $\cv<H(\alpha)$,when $0<g<1$, the launch price in both models will decrease with $k$. 
However, once $g = 1$, $l$ will no longer vary with $k$. 
In other words, when the government subsidy covers the full insurance, the launch price is no longer affected by the cost of effort.
(ii) Secondly, government subsidies have improved supply chain performance for both model IG and BG.
Specifically, when $\cv<H(\alpha)$, as government subsidies increase, the probability of a successful launch increases, premium rate decreases, launch price rises, revenues increase for both SO and VM, and social welfare increases.
However, when $\cv>H(\alpha)$, government subsidies only serves to enhance the SO's profit and social welfare.

\subsubsection{Values of applying both BCT and government subsidies}
After deriving the equilibrium decisions in SSC under Models G and Model BG, we now explore the values of BCT with government subsidies, which is defined as follows: 
\begin{eqnarray}\label{eq:value_bg}
	\begin{aligned}
		V_{x}^{BG}&=x^{BG}-x^{IG}\\
	\end{aligned}
\end{eqnarray}

By comparing Model BG and Model IG, we report the results in \reftab{tab:value_decision_bg} and \reftab{tab:value_profit_bg} which leading to \refprop{prop:value_decision_bg} and \refprop{prop:value_profit_bg}.
\begin{prop} \label{prop:value_decision_bg}
	Given $\kb$, $k$, $\theta$, $g$, $b$, then $e^{BG}>e^{IG}$, $r^{BG}<r^{IG}$, $l^{BG}>l^{IG}$, $p^{BG}>p^{IG}$.	
\end{prop}

The above results in \refprop{prop:value_decision_bg} are similar to those in \refprop{prop:value_decision_b}. 
For given $\kb$, $k$, $\theta$, $g$, and $b$, under the government subsidies, the BCT helps to increase the probability of successful launch $e$, the retail price $p$, and decrease the premium rate $r$.
When the cost of vehicle is high, the effect of blockchain in increasing launch price is weakened by $\frac{\alpha g(k-\kb)}{(1-\alpha)^2}$ as shown in \reftab{tab:value_decision}, compared with the case without subsidies.

\begin{prop} \label{prop:value_profit_bg}
	Given $\kb$, $k$, $\theta$, $g$, $b$: 
	\begin{enumerate}[(i)]
		\item
		If $\csb ~ \big( \begin{smallmatrix} < \\ =\\> \end{smallmatrix}  \big)~ \min\{\frac{k\lambda ^2-\kb \psi^2}{128k\kb (1-\alpha)^2},\frac{k(\mu-\alpha \kb)[\lambda-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\psi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}\}$,
		then we have: $V_{ SO}^{BG}~ \big(\begin{smallmatrix} > \\ =\\< \end{smallmatrix} \big) ~0$;
		\item
		When $\cv <H(\alpha)$, if $\cvb~ \big(\begin{smallmatrix} < \\ =\\> \end{smallmatrix} \big) ~\frac{k\lambda ^2-\kb \psi^2+32\alpha k \kb(\lambda-\psi)}{256k\kb (1-\alpha)^2} $ , for $\cv <H(\alpha$)
		then we have: $V_{VM}^{BG}~ \big(\begin{smallmatrix} > \\ =\\< \end{smallmatrix} \big) ~ 0$;
		when $\cv \geq H(\alpha)$, $V_{VM}^{BG} \equiv 0$
		\item
		$V_{CS}^{BG}>0$
		\item 
		When $\cv <H(\alpha)$, if $\csb+\cvb ~ \big( \begin{smallmatrix} < \\ =\\> \end{smallmatrix}  \big) \frac{3k\lambda ^2-3\kb \psi^2+32\alpha k \kb(\lambda-\psi)}{256k\kb (1-\alpha)^2}+\frac{b^2+2b}{8}  $, then we have $V_{SW}^{BG} ~ \big(\begin{smallmatrix} > \\ =\\< \end{smallmatrix} \big) ~ 0$;
		when $\cv \geq H(\alpha)$, if $\csb ~ \big(\begin{smallmatrix} < \\ =\\> \end{smallmatrix} \big) ~  \frac{k(\mu-\alpha \kb)[\lambda-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\psi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}+\frac{b^2+2b}{8}$, then we have $V_{SW}^{BG} ~ \big(\begin{smallmatrix} > \\ =\\< \end{smallmatrix} \big) ~ 0$.
	\end{enumerate}
\end{prop}

Compared with Model IG, the BCT in Model BG helps to increase the profit of SO and the welfare of society when the cost of BCT is not high.
For the VM, when $\cv<H(\alpha)$, he will benefit from the adoption of inexpensive BCT.
But he will not adopt BCT if it is too costly.
For customers, the consumer surplus will be higher once the BCT is adopted.
\begin{figure}[H]
	\centering
	\begin{subfigure}[b]{0.4\textwidth}
		\includegraphics[width=\textwidth]{sw1}
		\caption{$C_V<H(\alpha)$}
		\label{fig:sw1}
	\end{subfigure}
	\qquad
	~ %add desired spacing between images, e. g. ~, \quad, \qquad, \hfill etc. 
	%(or a blank line to force the subfigure onto a new line)
	\begin{subfigure}[b]{0.4\textwidth}
		\includegraphics[width=\textwidth]{sw2}
		\caption{$C_V \geq H(\alpha)$}
		\label{fig:sw2}
	\end{subfigure}
	\caption{The value of blockchain for social welfare with (i.e., $V_{SW}^{GB}$: the light grey area with the overlapping part enclosed by line $SW^{IG}$ and line $SW^{BG}$) and without government subsidies (i.e., $V_{SW}^B$: the dark grey area with the overlapping part enclosed by line $SW^I$ and line $SW^B$), when $k=0.8$, $\kb=0.6$,  $\cv=0.01$, $\cs=0.1$, $ \theta=0.5$, $b=0.9$, $g=0.5$, $\alpha=0.2$, $(\csb+\cvb)_1=\frac{3k\eta ^2-3\kb \phi^2+32\alpha k \kb(\eta-\phi)}{256k\kb (1-\alpha)^2}+\frac{b^2+2b}{8} $, $(\csb+\cvb)_2=\frac{3k\lambda ^2-3\kb \psi^2+32\alpha k \kb(\lambda-\psi)}{256k\kb (1-\alpha)^2}+\frac{b^2+2b}{8} $, $(\csb)_3= \frac{k(\mu-\alpha \kb)[\eta-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\phi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}+\frac{b^2+2b}{8}$,  $(\csb)_4=\frac{k(\mu-\alpha \kb)[\lambda-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\psi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}+\frac{b^2+2b}{8}$ . 
	}\label{fig:value_sw}
\end{figure}

Note that the BCT-adoption thresholds given by \refprop{prop:value_profit_bg} are higher than those listed in \refprop{prop:value_profit_b}.
This means, government subsidies help improve the affordability of the BCT. 
From another point of view, BCT adoption also amplifies the efficiency of government subsidies, according to the amplifications shown in \reftab{tab:value_profit}.

In conclusion, compared with the government subsidies case (Model IG), adopting BCT under government subsidies can increase the successful launch probability, and achieve an all-win situation where all SSC members benefit from low-cost BCT.
Besides, compared with the value of BCT without subsidies ($V_x^{B}$), the affordability of BCT will be improved by government subsidies, and the increase in launch price will lower, which means the value of the government will be magnify as shown in \reffig{fig:value_sw} (e.t., $(\csb+\cvb)_2>(\csb+\cvb)_1$ and $(\csb)_4>(\csb)_3$).
It implies that government subsidies are more likely to be preferred after adopting BCT.

\begin{table*}[htbp]
	\scriptsize
	%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
	\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
	\caption{\label{tab:value_decision_bg} Values of BCT with government subsidies on optimal decisions.}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{@{\extracolsep{1pt}}l*{14}{l}@{}}		
		\toprule
		&{Situation}&{$V_{ e^*}^{BG}$}&{$V_{ r^*}^{BG}$}&{$V_{ l^*}^{BG}$}&{$V_{ p^*}^{BG}$} \\
		\midrule
		Value & 	
		{$\cv < H(\alpha)$ } & 			   
		$\frac{k[(1+b)^2+4\theta]-\kb(1+4\theta)}{16k\kb}>0$&
		$-\beta\frac{k[(1+b)^2+4\theta]-\kb(1+4\theta)}{16k\kb}<0$&
		$\frac{(1-\alpha)(b^2+2b)+8\alpha(1-g)(k-\kb)}{8(1-\alpha)^2}>0$&
		$\frac{b}{2}>0$\\
		&{$\cv \geq H(\alpha)$ }&
		$\frac{k\mu-\kb \omega}{k\kb(1-\alpha)}>0$&
		$-\beta$$\frac{k\mu-\kb \omega}{k\kb(1\alpha)}<0$&
		$\frac{2(\mu-\omega)+2\alpha(k-\kb)}{(1-\alpha)^2}>0$&
		$\frac{b}{2}>0$\\
		\bottomrule			
	\end{tabular}
\end{table*}


\begin{table*}[htbp]
	\scriptsize
	%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
	\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
	\caption{\label{tab:value_profit_bg} Values of BCT with government subsidies on members' payoffs.}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{@{\extracolsep{1pt}}l*{14}{l}@{}}		
		\toprule
		&{Situation}&{$V_{ SO}^{BG}$}&{$V_{VM}^{BG}$}&{$V_{CS}^{BG}$}&{$V_{SW}^{BG}$} \\
		\midrule
		Value & 	
		{$\cv < H(\alpha)$ } & 			   
		$\frac{k\lambda ^2-\kb \psi^2}{128k\kb (1-\alpha)^2}-\csb$&
		$\frac{k\lambda ^2-\kb \psi^2+32\alpha k \kb(\lambda-\psi)}{256k\kb (1-\alpha)^2}-\cvb$&
		$\frac{b^2+2b}{8}$&
		$\frac{3k\lambda ^2-3\kb \psi^2+32\alpha k \kb(\lambda-\psi)}{256k\kb (1-\alpha)^2}+\frac{b^2+2b}{8}-\csb-\cvb$\\
		&{$\cv \geq H(\alpha)$ }&
		$\frac{k(\mu-\alpha \kb)[\lambda-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\psi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}-\csb$&
		$0$&
		$\frac{b^2+2b}{8}$&
		$\frac{k(\mu-\alpha \kb)[\lambda-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\psi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}+\frac{b^2+2b}{8}-\csb$\\
		\bottomrule			
	\end{tabular}
\end{table*}

%
%Furthermore, we compare the values of BCT under government subsidies with values of BCT without subsidies to explore the difference between adopting BCT impacted by the government subsidies.
%For a clearer comparison, we built $\Delta V_i$ as follows and summarize the outcomes in \reftab{tab:value_decision} and \reftab{tab:value_profit}.
%
%\textcolor{red}{If we look at the impacts of having the penalty scheme under the case with technologies, we will find that the government’s use of penalty scheme will yield the following: (i) The cyber-security level is higher than the case without penalty scheme. (ii) Both the supplier and consumer are benefited from the scheme than without penalty scheme. (iii) The e-tailer’s profit is hurt than without penalty scheme.}
%
%In order to explore the impact of government subsidized with BCT, we define the following terms $\Delta V_{ SO}$, $\Delta V_{VM}$, $\Delta CS$, and $\Delta SW$, which represent the benefits that government subsidies and BCT bring to the SO, the VM, customers, and the society, respectively. 
%
%\begin{eqnarray}\label{eq:value_bg}
%	\begin{aligned}
%		\Delta V_{ SO}&=(\pbgs-\pgs)-(\pbs-\pis)\\
%		\Delta V_{VM}&=(\pbgv-\pgv)-(\pbv-\piv)\\
%		\Delta V_{CS}&=(CS^{BG}-CS^{IG})-(CS^{B}-CS^I)\\
%		\Delta V_{SW}&=(SW^{BG}-SW^{IG})-(SW^{B}-SW^I)\\
%	\end{aligned}
%\end{eqnarray}
%
%\textcolor{red}{Furthermore, focusing on the thresholds (i.e., T for the case without technologies and TIT for the case with technologies) that determine whether adopting the government’s penalty scheme is beneficial to social welfare, we have the following findings: If F is relatively small and BCR > 1, then TIT is smaller than T. }

\begin{table*}[htbp]
	\scriptsize
	%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
	\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
	\caption{\label{tab:value_decision} The increases in the value of BCT on optimal decisions under government subsidies.}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{@{\extracolsep{1pt}}l*{14}{l}@{}}		
		\toprule
		&{Situation}&{$\Delta V_{ e^*}^B$}&{$\Delta V_{ r^*}^B$}&{$\Delta V_{ l^*}^B$}&{$\Delta V_{ p^*}^B$} \\
		\midrule
		$\Delta$Value & 	
		{$\cv < H(\alpha)$ } & 			   
		$0$&
		$0$&
		$\frac{-\alpha g(k-\kb)}{(1-\alpha)^2}<0$&
		$0$\\
		&{$\cv \geq H(\alpha)$ }&
		$0$&
		$0$&
		$0$&
		$0$\\
		\bottomrule			
	\end{tabular}
\end{table*}


\begin{table*}[htbp]
	\scriptsize
	%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
	\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
	\caption{\label{tab:value_profit} The increases in the value of BCT on on members' payoffs under government subsidies.}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{@{\extracolsep{1pt}}l*{14}{l}@{}}		
		\toprule
		&{Situation}&{$\Delta V_{ SO}^B$}&{$\Delta V_{VM}^B$}&{$\Delta V_{CS}^B$}&{$\Delta V_{SW}^B$} \\
		\midrule
		$\Delta$Value & 	
		{$\cv < H(\alpha)$ } & 			   
		$\frac{\alpha  g [(1-\alpha ) b^2+2 (1-\alpha ) b+4 \alpha  (2-g) (k-\kb)]}{8 (1-\alpha )^2}>0$&
		$\frac{\alpha  g [(1-\alpha ) b^2+2 (1-\alpha ) b-4 \alpha  (2+g) (k-\kb)]}{16 (1-\alpha )^2}>0$&
		$0$&
		$\frac{\alpha  g [3(1-\alpha ) b^2+6(1-\alpha ) b+4 \alpha  (2-3g) (k-\kb)]}{16 (1-\alpha )^2}>0$\\
		&{$\cv \geq H(\alpha)$ }&
		$\frac{2\alpha g[\alpha(k-\kb)-\omega+\mu]}{(-1 + \alpha)^2}>0$&
		$0$&
		$0$&
		$\frac{2\alpha g[\alpha(k-\kb)-\omega+\mu]}{(-1 + \alpha)^2}>0$\\
		\bottomrule			
	\end{tabular}
\end{table*}

\section{Extended models}\label{sec:extensions}
\subsection{Marginal cost of adopting BCT}\label{extend:model_c}
In the models above, we assume the cost of BCT is a lump sum neglecting the marginal cost of BCT to acquire and store data, which may not be accurate in practice.
Thus, we extend the blockchain models considering the marginal cost of adopting BCT denoted by $c$.
We verify the robustness of our findings by exploring two cases that 
(i) blockchain-embedded satellite launch supply chain with insurance (Model B-c)
(ii) blockchain-embedded satellite launch supply chain with government-subsidized insurance (Model BG-c).


\subsubsection{Model B-c} 

According to the setting, the market demand of Model B-c can be written as follows:

\begin{eqnarray}\label{eq:bcd}
	%	\left\{
	\begin{aligned}
		D^{B-c} &= 1 \int_{p^{B-c}-b}^{1}{f\left( u \right) \mathrm{d} u}= 1-p^{B-c}+b \\
	\end{aligned}
	%	\right.
\end{eqnarray}


Therefore, the members' payoffs can be measured as follows:
\begin{eqnarray}
	\begin{aligned}
		\pbcs &= e(p-c)D^{B-c} -[\alpha + e(1-\alpha) ]l - (r-g) (\cs + \alpha l) + (1-e)\beta (\cs + \alpha l)- \cs-\csb,\label{eq:bso:payoff}\\
		\pi_I^{B-c}&= r (\cs + \alpha l)-(1-e)\beta (\cs + \alpha l),\\
		\pbcv&=[\alpha + e (1 - \alpha) ]l - (1 - e) \theta - (\kb e^2 + \cv)-\cvb,\label{eq:bvm:payoff}\\
		s.t.~\pbcv &\geq 0.
	\end{aligned}
\end{eqnarray}

Note, the only difference between Model B-c and Model B is that the BCT's marginal cost occurs to SO.
We solve the derivation and summarize the outcomes in \reftab{tab:modelbc_decisions}.

\begin{table*}[htbp]
	\scriptsize
	%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
	\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
	\caption{\label{tab:modelbc_decisions} The equilibrium outcomes in Model B-c.}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{@{\extracolsep{1pt}}l*{14}{c}@{}}		
		\toprule
		& \multicolumn{1}{c}{$\cv < H(\alpha)$ } & \multicolumn{1}{c}{$\cv \geq H(\alpha)$ }  \\
		\midrule
		Effort of VM exerting $e^*$& 
		$\frac{\eta -C}{16 (1-\alpha )\kb}$ & 
		$\frac{\mu-\alpha \kb }{(1-\alpha)\kb}$  \\
		Launch price $l^*$&
		$l^*=l_{S}=\frac{\eta-8\theta(1-\alpha)-C}{8(1-\alpha)^2}$&
		$ l^*=l_{VA}= \frac{2\mu-2\alpha \kb-(1-\alpha) \theta}{(1-\alpha)^2}$\\ 
		Retail price $p^*$&
		$\frac{1+b+c}{2}$&
		$\frac{1+b+c}{2}$\\
		Premium rate $r^*$&
		$\beta(1-\frac{\eta-C}{16(1-\alpha)\kb})$&
		$\beta\frac{\kb-\mu}{(1-\alpha)\kb}$\\
		SO's profit $\pbcs$&
		$\frac{\eta^2-C(C-2\eta)}{128(1-\alpha)^2\kb}+\frac{\alpha \theta}{1-\alpha} -\cs-\csb$&
		$\frac{(\mu-\alpha \kb)(\eta+8\alpha \kb-8\mu-C)}{4(1-\alpha )^2\kb}+\frac{\alpha \theta}{1-\alpha}-\cs-\csb$\\
		VM's profit $\pbcv$&
		$\frac{\eta^2+32\alpha \kb\eta-C(C-2\eta-32\alpha \kb)}{256(1-\alpha)^2\kb}-\frac{ \theta}{1-\alpha}-\cv-\cvb$&
		$0$\\
		Consumer surplus $CS^{B-c}$&
		$\frac{(1+b-c)^2}{8}$&
		$\frac{(1+b-c)^2}{8}$&\\
		Social welfare $SW^{B-c}$&
		$\frac{3\eta^2+32\alpha \kb\eta-C(3C-6\eta-32\alpha \kb)}{256(1-\alpha)^2\kb}- \theta-\cs-\cv-\csb-\cvb+\frac{(1+b-c)^2}{8}$&
		$\frac{(\mu-\alpha \kb)(\phi+8\alpha \kb-8\mu-C)}{4(1-\alpha )^2\kb}+\frac{\alpha \theta}{1-\alpha}-\cs-\csb+\frac{(1+b-c)^2}{8}$\\
		\bottomrule			
	\end{tabular}
	\begin{tablenotes}
		\item To avoid complicated writing, we define 
		$\eta=(1-\alpha)(1+b)^2+4(1-\alpha)\theta-8\alpha \kb$, 
		$\mu=\sqrt{(1-\alpha)^2\kb (\cv+\cvb)+\alpha ^2{\kb}^2-(1-\alpha)\kb \theta}$,
		$C=(1-\alpha)c(2+2b-c)$.
	\end{tablenotes}
\end{table*}

To explore the effect of blockchain marginal cost on the equilibrium outcomes, we compare Model B-c with Model B and obtain \refprop{prop:modelbc_vs_b}.

\begin{prop} \label{prop:modelbc_vs_b}
	Under Model B-c, the satellite launch supply chain adopts the BCT with insurance considering the marginal cost of BCT.
	
	 Compared with Model B,
	(i) when $\cv<H(\alpha)$, 
	(a) $e^{B-c}<e^B$, $l^{B-c}<l^B$, $r^{B-c}>r^B$, $p^{B-c}>p^B$; 
	(b) if $0< c< 1+b-\sqrt{\frac{(1-\alpha)(1+b)^2-2\eta}{1-\alpha}}$, $\pi_S^{B-c}>\pi_S^B$; otherwise, $\pi_S^{B-c} \leq  \pi_S^B$;
	if $0<c<1+b-\sqrt{\frac{(1-\alpha)(1+b)^2-2(\eta+16\alpha \kb)}{1-\alpha}}$, $\pi_V^{B-c}>\pi_V^B$; otherwise, $\pi_V^{B-c} \leq \pi_V^B$;
	$CS^{B-c}<CS^{B}$;
	if $0<c<1+b-\sqrt{\frac{3(1-\alpha)(1+b)^2-2(3\eta+16\kb)}{3(1-\alpha)}}$, $\pi_{SW}^{B-c}>\pi_{SW}^B$; otherwise, $\pi_{SW}^{B-c} \leq \pi_{SW}^B$;

	(ii) when $\cv \geq H(\alpha)$, 
	(a) $e^{B-c}=e^B$, $l^{B-c}=l^B$, $r^{B-c}=r^B$, $p^{B-c}>p^B$; 
	(b) $\pi_S^{B-c}< \pi_S^B$; $\pi_V^{B-c} = \pi_V^B=0$; $CS^{B-c}<CS^{B}$; $\pi_{SW}^{B-c} < \pi_{SW}^B$.
\end{prop}


\refprop{prop:modelbc_vs_b} indicates the effect of marginal cost of BCT by comparing Model B-c and Model B and give us new findings.
It implies that in the case of $\cv<H(\alpha)$, the presence of the BCT marginal cost in the satellite launch supply chain means that SO prefers to pay a lower launch price, the VM exerts less effort to make the launch successful, the SO has to bear higher insurance rates, and consumers suffer a higher retail price.
Since the marginal cost of BCT can lead to both an increase in retail price and a decrease in market demand, there exists thresholds regarding $c$ for comparing members' profits between Model B-c and Model B.
The tradeoff between the higher retail price and the lower market demand affects the change in total profit eventually. 
In the first case ($\cv<H(\alpha)$), when the marginal cost is low, the supply chain participants in Model B-c have higher returns. 
Once the marginal cost exceeds a certain threshold, the payoffs of participants in Model B-c are lower than those in Model B. 
For consumers, once the marginal cost exists, consumer surplus is impaired because they need to pay a higher retail price.

However, when the SO chooses an expensive vehicle ($\cv \geq H(\alpha)$), only the retail price is higher than that in Model B, and the others are equal to that in Model B, which do not affect by $c$.
This is because the VM sets the launch price instead of the SO in this scenario. 
Therefore, transferring the marginal cost of BCT to consumers is the only way for the SO to make a profit. This treatment is similar to transferring the variable price per product unit in a traditional supply chain.
For the payoff, all participants except the VM suffer a loss of profits due to the presence of marginal costs. The VM only maintains break-even in this scenario, the same as Model B.

Further, to explore whether the value of BCT to the launch supply chain changes after considering marginal costs, i.e., to verify the robustness of \refprop{prop:value_decision_b} and \refprop{prop:value_profit_b}, we conduct comparison between Models B-c and Model I nextly.

\begin{prop} \label{prop:modelbc_vs_i}
	Under Model B-c, the satellite launch supply chain adopts the BCT with insurance considering the marginal cost of BCT.
    
    Compared with Model I,
    (i) when $\cv<H(\alpha)$, 
	(a) if $0<c<1+b-\sqrt{\frac{(1+4\theta)\kb}{k}-4 \theta }$, $e^{B-c}>e^I$, $r^{B-c}<r^I$; otherwise, $e^{B-c}\leq e^I$, $r^{B-c}\geq r^I$; 
	if $0<c<1+b-\sqrt{1-\frac{8\alpha(k-\kb)}{1-\alpha}}$, $l^{B-c}>l^I$; otherwise, $l^{B-c}\leq l^I$;
	if $0<c<b$, $p^{B-c}>p^I$, otherwise, $p^{B-c} \leq p^I$
	(b) if $0<c<1 + b - \sqrt{\frac{(1-\alpha)(1+b)^2-2\eta}{
			1 - \alpha}} $ and $\csb<\frac{k\eta ^2-\kb \phi^2}{128k\kb (1-\alpha)^2}$, $\pbcs > \pis$; otherwise, $\pbcs \leq \pis$;
		if $0<c<1+b-\sqrt{\frac{(1-\alpha)(1+b)^2-2\eta-32\alpha \kb}{1-\alpha }}$ and $\cvb<\frac{k\eta ^2-\kb \phi^2+32\alpha k \kb(\eta-\phi)}{256k\kb (1-\alpha)^2}$, $\pbcv>\piv$; otherwise, $\pbcv \leq \piv$; 
		if $0<c<b$, $CS^{B-c}> CS^I$; otherwise, $CS^{B-c} \leq CS^I$;
		if $0<c<1+b-\sqrt{\frac{3(1-\alpha)(1+b)^2-6\eta-32\alpha \kb}{3(1-\alpha)}}$ and $\csb+\cvb < \frac{3k\eta ^2-3\kb \phi^2+32\alpha k \kb(\eta-\phi)}{256k\kb (1-\alpha)^2}+\frac{b^2+2b}{8}$, $SW^{B-c}>SW^I$; otherwise, $SW^{B-c} \leq SW^I$.
		
	(ii) when $\cv \geq H(\alpha)$, 
	(a) $e^{B-c}>e^I$, $l^{B-c}>l^I$, $r^{B-c}<r^I$; if $0<c<b$, $p^{B-c}>p^I$; otherwise,  $p^{B-c} \leq p^I$;
	(b) if	$\csb<\frac{k(\mu-\alpha \kb)[\eta-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\phi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}$, $\pbcs> \pis$; otherwise, $\pi_S^{B-c} \leq \pis$;
	$\pi_V^{B-c} = \piv=0$;  
    if $0<c<b$, $CS^{B-c}> CS^I$; otherwise, $CS^{B-c} \leq CS^I$;
	if $\csb<\frac{k(\mu-\alpha \kb)[\eta-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\phi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}$ and $0<c<b$, $\pi_{SW}^{B-c} > \pi_{SW}^I$; otherwise, $\pi_{SW}^{B-c} \leq \pi_{SW}^I$.
\end{prop}

\refprop{prop:modelbc_vs_i} shows that when the BCT variation cost is within a certain interval, comparing Model B-c and Model I, the launch success probability increases, the launch price increases, the retail price increases, and the insurance rate decreases. 
This result is the same as the outcomes in \refprop{prop:value_decision_b} (comparing Model B with Model I).


Moreover, by comparing the members' profits in Model B-c and Model I, we also find that when the marginal cost $c$ under a threshold and the cost of BCT is low, all the members will benefit from adopting BCT.

Therefore, by comparing Model B-c and Model I in \refprop{prop:modelbc_vs_i}, our findings on the value of BCT are proved to be robust.




\subsubsection{Model BG-c}

Similar to Model BG, we build Model BG-c considering the marginal cost of BCT, which can be written as follows:

\begin{eqnarray}\label{eq:bgcd}
	%	\left\{
	\begin{aligned}
		D^{BG-c} &= 1 \int_{p^{BG-c}-b}^{1}{f\left( u \right) \mathrm{d} u}= 1-p^{BG-c}+b \\
	\end{aligned}
	%	\right.
\end{eqnarray}


Therefore, the members' payoffs can be measured as follows:
\begin{eqnarray}
	\begin{aligned}
		\pbgcs &= e(p-c)D^{BG-c} -[\alpha + e(1-\alpha) ]l - (r-g) (\cs + \alpha l) + (1-e)\beta (\cs + \alpha l)- \cs-\csb,\label{eq:bso:payoff}\\
		\pi_I^{BG-c}&= r (\cs + \alpha l)-(1-e)\beta (\cs + \alpha l),\\
		\pbgcv&=[\alpha + e (1 - \alpha) ]l - (1 - e) \theta - (\kb e^2 + \cv)-\cvb,\label{eq:bvm:payoff}\\
		s.t.~\pbgcv &\geq 0.
	\end{aligned}
\end{eqnarray}

Note, the only difference between Model BG-c and Model BG is that the BCT's marginal cost occurs to SO.
We solve the derivation and summarize the outcomes in \reftab{tab:modelbgc_decisions}.


\begin{table*}[htbp]
	\scriptsize
	%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
	\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
	\caption{\label{tab:modelbgc_decisions} The equilibrium outcomes in Model BG-c.}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{@{\extracolsep{1pt}}l*{14}{c}@{}}		
		\toprule
		& \multicolumn{1}{c}{$\cv < H(\alpha)$ } & \multicolumn{1}{c}{$\cv \geq H(\alpha)$ }  \\
		\midrule
		Effort of VM exerting $e^*$& 
		$\frac{\lambda -C}{16 (1-\alpha )\kb}$ & 
		$\frac{\mu-\alpha \kb }{(1-\alpha)\kb}$  \\
		Launch price $l^*$&
		$l^*=l_{S}=\frac{\lambda-8\theta(1-\alpha)-C}{8(1-\alpha)^2}$&
		$ l^*=l_{VA}= \frac{2\mu-2\alpha \kb-(1-\alpha) \theta}{(1-\alpha)^2}$\\ 
		Retail price $p^*$&
		$\frac{1+b+c}{2}$&
		$\frac{1+b+c}{2}$\\
		Premium rate $r^*$&
		$\beta(1-\frac{\lambda-C}{16(1-\alpha)\kb})$&
		$\beta\frac{\kb-\mu}{(1-\alpha)\kb}$\\
		SO's profit $\pbcs$&
		$\frac{\lambda^2-C(C-2\lambda)}{128(1-\alpha)^2\kb}+\frac{(1-g)\alpha \theta}{1-\alpha} -(1-g)\cs-\csb$&
		$\frac{(\mu-\alpha \kb)(\lambda+8\alpha \kb-8\mu-C)}{4(1-\alpha )^2\kb}+\frac{(1-g)\alpha \theta}{1-\alpha}-(1-g)\cs-\csb$\\
		VM's profit $\pbcv$&
		$\frac{\lambda^2+32\alpha \kb\lambda-C(C-2\lambda-32\alpha \kb)}{256(1-\alpha)^2\kb}-\frac{ \theta}{1-\alpha}-\cv-\cvb$&
		$0$\\
		Consumer surplus $CS^{B-c}$&
		$\frac{(1+b-c)^2}{8}$&
		$\frac{(1+b-c)^2}{8}$&\\
		Social welfare $SW^{B-c}$&
		$\frac{3\lambda^2+32\alpha \kb\lambda-C(3C-6\lambda-32\alpha \kb)}{256(1-\alpha)^2\kb}- \frac{\theta[1-(1-g)\alpha]}{1-\alpha}-(1-g)\cs-\cv-\csb-\cvb+\frac{(1+b-c)^2}{8}$&
		$\frac{(\mu-\alpha \kb)(\phi+8\alpha \kb-8\mu-C)}{4(1-\alpha )^2\kb}+\frac{(1-g)\alpha \theta}{1-\alpha}-(1-g)\cs-\csb+\frac{(1+b-c)^2}{8}$\\
		\bottomrule			
	\end{tabular}
	\begin{tablenotes}
		\item To avoid complicated writing, we define 
		$\lambda=(1-\alpha)(1+b)^2+4(1-\alpha)\theta-8\alpha \kb$, 
		$\mu=\sqrt{(1-\alpha)^2\kb (\cv+\cvb)+\alpha ^2{\kb}^2-(1-\alpha)\kb \theta}$,
		$C=(1-\alpha)c(2+2b-c)$.
	\end{tablenotes}
\end{table*}

To explore the effect of blockchain marginal cost on the equilibrium outcomes under government subsidies, we compare model BG-c with Model BG and obtain \refprop{prop:modelbgc_vs_bg}.

\begin{prop} \label{prop:modelbgc_vs_bg}
	Under Model BG-c, the satellite launch supply chain adopts the BCT with government-subsidies insurance considering the marginal cost of BCT.
	
	Compared with Model BG,
	(i) when $\cv<H(\alpha)$, 
	(a) $e^{BG-c}<e^{BG}$, $l^{BG-c}<l^{BG}$, $r^{BG-c}>r^{BG}$, $p^{BG-c}>p^{BG}$; 
	(b) if $0< c< 1+b-\sqrt{\frac{(1-\alpha)(1+b)^2-2\lambda}{1-\alpha}}$, $\pbgcs>\pbgs$; otherwise, $\pbgcs \leq \pbgs $;
	if $0<c<1+b-\sqrt{\frac{(1-\alpha)(1+b)^2-2(\lambda+16\alpha \kb)}{1-\alpha}}$, $\pbgcv>\pbgv$; otherwise, $\pbgcv \leq \pbgv$;
	$CS^{BG-c}<CS^{BG}$;
	if $0<c<1+b-\sqrt{\frac{3(1-\alpha)(1+b)^2-6\lambda-32\kb}{3(1-\alpha)}}$, $\pi_{SW}^{BG-c}>\pi_{SW}^{BG}$; otherwise, $\pi_{SW}^{BG-c} \leq \pi_{SW}^{BG}$;
	(ii) when $\cv \geq H(\alpha)$, 
	(a) $e^{BG-c}=e^{BG}$, $l^{BG-c}=l^{BG}$, $r^{BG-c}=r^{BG}$, $p^{BG-c}>p^{BG}$; 
	(b) $\pi_S^{BG-c}< \pi_S^{BG}$; $\pi_V^{BG-c} = \pi_V^{BG}=0$; $CS^{BG-c}<CS^{BG}$; $\pi_{SW}^{BG-c} < \pi_{SW}^{BG}$.
\end{prop}

\refprop{prop:modelbgc_vs_bg} indicates the effect of marginal cost of BCT under government subsidies by comparing Model BG-c and Model BG, which is similar to. 

\refprop{prop:modelbgc_vs_bg} shows that the impact of BCT marginal cost under government subsidies derived by comparing model BG-c with model BG.
It can be seen that the results are very similar to  \refprop{prop:modelbc_vs_b}, the only difference being that the specific threshold of marginal cost becomes higher with government subsidies. 
That means the affordability of marginal costs is enhanced with the support of government subsidies.


Moreover, we compare Model BG-c with Model BG to explore whether the marginal cost changes the value of BCT under government subsidies, i.e., to verify the robustness of \refprop{prop:value_decision_bg} and \refprop{prop:value_profit_bg}.

\begin{prop} \label{prop:modelbgc_vs_g}
	Under Model BG-c, the satellite launch supply chain adopts the BCT with government-subsidies insurance considering the marginal cost of BCT.
	
	Compared with Model IG,
	(i) when $\cv<H(\alpha)$, 
	(a) if $0<c<1+b-\sqrt{\frac{(1+4\theta)\kb}{k}-4 \theta }$, $e^{BG-c}>e^{IG}$, $r^{BG-c}<r^{IG}$; otherwise, $e^{B-c}\leq e^I$, $r^{BG-c}\geq r^{IG}$; 
	if $0<c<1+b-\sqrt{1-\frac{8\alpha(1-g)(k-\kb)}{1-\alpha}}$, $l^{BG-c}>l^{IG}$; otherwise, $l^{BG-c}\leq l^{IG}$;
	if $0<c<b$, $p^{BG-c}>p^{IG}$, otherwise, $p^{BG-c} \leq p^{IG}$
    (b) if $0<c<1 + b - \sqrt{\frac{(1-\alpha)(1+b)^2-2\lambda}{
	1 - \alpha}} $ and $\csb<\frac{k\lambda ^2-\kb \psi^2}{128k\kb (1-\alpha)^2}$, $\pbgcs > \pgs$; otherwise, $\pbgcs \leq \pgs$;
	if $0<c<1+b-\sqrt{\frac{(1-\alpha)(1+b)^2-2\lambda-32\alpha \kb}{1-\alpha }}$ and $\cvb<\frac{k\lambda ^2-\kb \psi^2+32\alpha k \kb(\lambda-\psi)}{256k\kb (1-\alpha)^2}$, $\pbgcv>\pgv$; otherwise, $\pbgcv \leq \pgv$; 
	if $0<c<b$, $CS^{BG-c}> CS^{IG}$; otherwise, $CS^{BG-c} \leq CS^{IG}$;
	if $0<c<1+b-\sqrt{\frac{3(1-\alpha)(1+b)^2 -6\lambda-32\alpha \kb}{3(1-\alpha)}}$ and $\csb+\cvb < \frac{3k\lambda ^2-3\kb \psi^2+32\alpha k \kb(\lambda-\psi)}{256k\kb (1-\alpha)^2}+\frac{b^2+2b}{8}  $, 
	$SW^{BG-c}>SW^{IG}$; otherwise, $SW^{BG-c} \leq SW^{IG}$.

	(ii) when $\cv \geq H(\alpha)$, 
	(a) $e^{BG-c}>e^{IG}$, $l^{BG-c}>l^{IG}$, $r^{BG-c}<r^{IG}$; if $0<c<b$, $p^{BG-c}>p^{IG}$; otherwise,  $p^{BG-c} \leq p^{IG}$;
	(b) if	$\csb<\frac{k(\mu-\alpha \kb)[\lambda-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\psi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}$, $\pbgcs> \pgs$; otherwise, $\pbgcs \leq \pgs$;
	$\pi_V^{BG-c} = \pgv=0$;  
	if $0<c<b$, $CS^{BG-c}> CS^{IG}$; otherwise, $CS^{BG-c} \leq CS^{IG}$;
	if $\csb<\frac{k(\mu-\alpha \kb)[\eta-8(\mu-\alpha \kb)]-\kb (\omega-\alpha k)[\phi-8(\omega-\alpha k)]}{4k\kb(1-\alpha)^2}$ and $0<c<b$, $\pi_{SW}^{BG-c} > \pi_{SW}^{IG}$; otherwise, $\pi_{SW}^{BG-c} \leq \pi_{SW}^{IG}$.
\end{prop}

The results in \refprop{prop:modelbgc_vs_g} are similar to \refprop{prop:modelbc_vs_i} that comparing Model BG-c and Model G,the launch success probability increases, the launch price increases, the retail price increases, and the insurance rate decreases with the BCT variation cost in a certain interval.
This result is the same as the outcomes in \refprop{prop:value_decision_bg} (comparing Model BG with Model IG).


Besides, by comparing members' profits in Model BG-c and Model IG, we also find that when the marginal cost $c$ under a threshold and the cost of BCT is low, all the members will benefit from adopting BCT under government subsidies.

Therefore, by comparing Model BG-c and Model IG, our findings in \refprop{prop:value_decision_bg} and \refprop{prop:value_profit_bg} about the value of BCT with the government subsidy are proved to be robust.


\subsection{Alliance}
Inspired by alliances in the real-world alliances, such as U.S. Space Enterprise Consortium and China Commercial Space Alliance, we extend the models to explore if an alliance strategy is a better to improve the effective of  satellite launch supply chain in this section.
On the basis of the main cases, we build three models: 
(i) the VM and SO form an alliance with launch insurance (Model IA); 
(ii) the VM and SO form an alliance with launch insurance under government subsidies(Model GA);
(iii) the VM and SO form an alliance with blockchain-embedded launch insurance (Model BA);
(iv) the VM and SO form an alliance with blockchain-embedded launch insurance under government subsidies (Model BGA).

In the above models, the VM and the SO attempt to maximize their respective benefits, VM by deciding the effort to be paid, and SO by determining the launch service price and retail price.
However, in the alliance strategy, VM and SO will act as a whole alliance to decide the efforts exert and the retail price.
Thus the market demand and payoff functions of Model IA can be written as follows:
\begin{eqnarray}
	%	\left\{
	\begin{aligned}
		D^{IA} &= 1 \int_{p^{IA}}^{1}{f\left( u \right) \mathrm{d} u}= 1-p^{IA} \\
	\end{aligned}
	%	\right.
\end{eqnarray}

\begin{eqnarray}
	\begin{aligned}
		\pia&= epD^{IA} -(1 - e) \theta  - r \cs  + (1-e)\beta \cs-\cs-\cv,\\
		\pi_I^{IA}&= r \cs -(1-e)\beta \cs.\\
	\end{aligned}
\end{eqnarray}

The functions of Model GA, Model BA, and model BGA are similar to Model IA which we omit here. 
By inverse solving, we obtain the equilibrium outcomes which are summarized in \reftab{tab:modelia_modelga_decisions} and \reftab{tab:modelba_modelbga_decisions}




\begin{table*}[htbp]
	\scriptsize
	%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
	\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
	\caption{\label{tab:modelia_modelga_decisions} The equilibrium outcomes in Model IA and Model GA.}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{@{\extracolsep{1pt}}l*{14}{c}@{}}		
		\toprule
		& \multicolumn{1}{c}{Model IA } & \multicolumn{1}{c}{Model GA  }   \\
%		\multicolumn{1}{c}{Model BA  } &\multicolumn{1}{c}{Model BGA  } \\
		\midrule
		Effort of SC exerting $e^*$& 
		$\frac{1+4\theta-4\beta \cs}{8k}$ &
		$\frac{1+4\theta-4\beta \cs}{8k}$  \\
%	   $\frac{(1+b)^2+4\theta-4\beta \cs}{8\kb}$&
%	   $\frac{(1+b)^2+4\theta-4\beta \cs}{8\kb}$ \\
		Retail price $p^*$&
		$\frac{1}{2}$&
		$\frac{1}{2}$\\
%		$\frac{1}{2}$\\
		Premium rate $r^*$&
		$\beta(1-\frac{1+4\theta-4\beta \cs}{8k})$&
		$\beta(1-\frac{1+4\theta-4\beta \cs}{8k})$\\
%		$\beta(1-\frac{(1+b)^2+4\theta-4\beta \cs}{8\kb})$	\\
		SC's profit $\pi_{SC}$&
		$\frac{(1+4\theta)^2-(4\beta \cs)^2}{64k}-\theta-\cs-\cv$&
		$\frac{(1+4\theta)^2-(4\beta \cs)^2}{64k}-\theta-(1-g)\cs-\cv$\\
%	    $\frac{[(1+b)^2+4\theta]^2-(4\beta \cs)^2}{64k}-\theta-\cs-\cv-\csb-\cvb$\\
		Consumer surplus $CS$&
		$\frac{1}{8}$&
		$\frac{1}{8}$\\
%		$\frac{1}{8}$\\
		Social welfare $SW$&
		$\frac{(1+4\theta)^2-(4\beta \cs)^2}{64k}-\theta-\cs-\cv+\frac{1}{8}$&
		$\frac{(1+4\theta)^2-(4\beta \cs)^2}{64k}-\theta-(1-g)\cs-\cv+\frac{1}{8}$\\
%		$\frac{[(1+b)^2+4\theta]^2-(4\beta \cs)^2}{64k}-\theta-\cs-\cv-\csb-\cvb+\frac{1}{8}$\\
		\bottomrule			
	\end{tabular}
\end{table*}

\begin{table*}[htbp]
	\scriptsize
	%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
	\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
	\caption{\label{tab:modelba_modelbga_decisions} The equilibrium outcomes in Model BA and Model BGA.}
	\centering
	\renewcommand{\arraystretch}{1.3}
	\begin{tabular}{@{\extracolsep{1pt}}l*{14}{c}@{}}		
		\toprule
		& \multicolumn{1}{c}{Model BA  } &\multicolumn{1}{c}{Model BGA  } \\
		\midrule
		Effort of SC exerting $e^*$& 
		$\frac{(1+b)^2+4\theta-4\beta \cs}{8\kb}$&
		$\frac{(1+b)^2+4\theta-4\beta \cs}{8\kb}$ \\
		Retail price $p^*$&
		$\frac{1+b}{2}$&
		$\frac{1+b}{2}$\\
		Premium rate $r^*$&
		$\beta(1-\frac{(1+b)^2+4\theta-4\beta \cs}{8\kb})$&
		$\beta(1-\frac{(1+b)^2+4\theta-4\beta \cs}{8\kb})$	\\
		SC's profit $\pi_{SC}$&
		$\frac{[(1+b)^2+4\theta]^2-(4\beta \cs)^2}{64\kb}-\theta-\cs-\cv-\csb-\cvb$&
		$\frac{[(1+b)^2+4\theta]^2-(4\beta \cs)^2}{64\kb}-\theta-(1-g)\cs-\cv-\csb-\cvb$\\
		Consumer surplus $CS$&
		$\frac{(1+b)^2}{8}$&
		$\frac{(1+b)^2}{8}$\\
		Social welfare $SW$&
		$\frac{[(1+b)^2+4\theta]^2-(4\beta \cs)^2}{64\kb}-\theta-\cs-\cv-\csb-\cvb+\frac{(1+b)^2}{8}$&
		$\frac{[(1+b)^2+4\theta]^2-(4\beta \cs)^2}{64\kb}-\theta-(1-g)\cs-\cv-\csb-\cvb+\frac{(1+b)^2}{8}$
		\\
		\bottomrule			
	\end{tabular}
\end{table*}
The outcomes above imply a difference that the optimal decisions are effected by the insurance market instead of the prepay rule.
That means, as the VM and SO form an alliance, the motivation of VM to improve the successful launch probability changes from the prepay ratio ($\alpha$) to the insurance claim ($\beta \cs$).
Thus, the less insurance covers, the more effort VM exerts. 
By comparing Model IA and Model I, model GA and Model IG, Model BA and Model B, Model BGA and Model BG, we get \refprop{prop:modela_vs_model}.

\begin{prop}\label{prop:modela_vs_model}
When the VM and the SO form an alliance, 

(i) comparing Model IA and Model I, 
if $\beta\cs<\frac{(1-\alpha)(1+4\theta)+8\alpha k }{ 8(1-\alpha)}$, then $e^{IA}>e^I$ and $\swia>SW^{I}$;

(ii) comparing Model GA and Model G,
if $\beta\cs<\frac{(1-\alpha)(1+4\theta)+8\alpha k(1-g)}{ 8(1-\alpha)}$, then $e^{GA}>e^{IG}$;
if $ (\beta\cs)^2<\frac{[(1-\alpha)(1+4\theta)+8\alpha k(1-g)]^2+32\alpha kg[(4\theta-1)(1-\alpha)+8\alpha k(1-g)]}{[8(1-\alpha)]^2} $, then  $\swga>SW^{IG}$;

(iii) comparing Model BA and Model B,
if $ \beta\cs<\frac{(1-\alpha)[(1+b)^2+4\theta]+8\alpha \kb }{8(1-\alpha)}$, $e^{BA}>e^B$ and $\swba > SW^{B}$;

(iv) comparing Model BGA and Model BG,
if $\beta\cs<\frac{(1-\alpha))[(1+b)^2+4\theta]+8\alpha \kb(1-g)}{8(1-\alpha)} $, $e^{BGA}>e^{BG}$;
if $ (\beta\cs)^2<\frac{\{(1-\alpha)[(1+b)^2+4\theta]+8\alpha \kb(1-g)\}^2+32\alpha \kb g\{[4\theta-(1+b)^2](1-\alpha)+8\alpha \kb(1-g)\} }{[8(1-\alpha)]^2}$,  $\swbga>SW^{BG}$.
\end{prop}

\refprop{prop:modela_vs_model} gives the specific insurance claim thresholds for the adoption of the alliance strategy under four scenarios.
Note that the retail price paid by the consumer and the consumer surplus remain the same, so the increased social welfare mainly comes from the increase in supply chain profits.

Therefore, when the insurance market is soft, it would be a wise idea to pursue an alliance strategy in the satellite launch supply chain. 
It will contribute to an increase in the probability of successful launches as well as to the improvement of social welfare.



\section{Conclusions}\label{sec:conclusions}
\subsection{Remarkable findings}
Nowadays, with the prosperity of commercial launches, more and more research is being conducted in the operation management of space. 
Motivated by the real-world government-subsidized launch insurance project, we explored the operations of the satellite launch supply chain with government-subsidized insurance. 
Firstly, we established the traditional insurance model (Model I) and the government-subsidized insurance model (Model IG). 
By deriving analytical results, we demonstrate the optimal decisions for each participant.
We have further uncovered the effect of the subsidies on different variables.
Finally, we built value models to investigate the benefit of subsidies, especially revealing the conditions under which one model outperforms the other.

However, we find that if only the government provides subsidies, the customers cannot benefit. 
So we investigate the blockchain applications in the space launch supply chain by building a blockchain-embedded insurance model (Model B), which has also been implemented in the real world. 
Besides, considering the high blockchain costs, we explored the scenario of adopting blockchain under government subsidies (Model BG).
At last, in order to measure the value of blockchain under different scenarios, we compare Model B with Model I and Model BG with Model IG. And we analyzed the change of blockchain impact under the government subsidy scenario.


As a concluding remark, we highlight the answers as follows:
 \begin{enumerate} [(1)]
\item Government subsidized launch insurance can achieve win-win in satellite launch supply chain and improve the social welfare. However, it is not always preferred to implement the government subsidy in all cases. 
When the government provides subsidies, it is necessary to screen satellite vendors, and only by subsidizing satellite launch activities with inexpensive vehicles can it effectively promote the development of the launch market. 
Otherwise, subsidies can only increase the profit of satellite operators but can not promote the launch success rate, which is not conducive to the optimal allocation of government funds.

\item The government subsidies have helped to establish positive feedback for the satellite launch market; 
that is, the satellite vendor is more willing to pay high launch price, so that the vehicle manufacturer is motivated to increase the probability of successful launches.

\item Once the government subsidy project is launched, the satellite operator will always get more from it than before. 
But for the vehicle manufacturer, only when the cost of vehicle is relatively low, his income will increase compared to before; otherwise, he cannot benefit from the subsidy program.
For consumers, there is no change in consumer surplus.
Therefore, the overall social welfare as the sum of the profit of the various subjects will increase.

\item In the blockchain-embedded model, the values that blockchain bring to the optimal decisions are similar to the government subsidy brings.
However, there is one difference to claim that the retail price has been increased and the market demand also increases.

\item Moreover, for the satellite, she will always benefit from the adoption of blockchain if its cost is relatively low.

\item However, the profitable condition for the vehicle to decide whether use the blockchain is not only the cost of blockchain is expensive but also the cost of vehicle manufacturing is low.

\item Significantly, the use of the blockchain launch platform will make the consumer surplus increase no matter in which situation.

\item Interestingly, the adoption of blockchain can increase the benefits of government subsidies. 
Besides, when the supply chain obtains the government subsidies, both the satellite operator and the vehicle manufacture can enhance the affordability of blockchain costs.
 \end{enumerate} 

\subsection{Managerial implications}
Analyzing the derived findings, we further propose the following managerial implications, which help form action plans for satellite operators, vehicle manufacturers, and the government.\par 
Satellite operator: It is the most effective to improve profit by applying for government insurance subsidies.
Moreover, the adoption of the blockchain-embedded launch platform will also enhance the profit when the cost of blockchain is low.\par 

Vehicle manufacturer: Only when vehicle costs are low can manufacturers indirectly enjoy the benefits of government subsidies.
Otherwise, the manufacturer will be nonprofitable.
However, it is worth noting that adopting blockchain technology to provide launch services is always beneficial for vehicle manufacturers, as it can increase the probability of a successful launch.
Besides, when the blockchain and vehicle manufacturing costs are low, adopting blockchain technology is the best strategy for the manufacturer, which will improve his profitability.\par 

Government:  Intuitively, government provision of insurance subsidies can improve social welfare. 
However, the excellent way to optimally allocate the limited subsidy funds is to disburse the subsidies to satellite operators who choose cost-effective vehicles. 
This is because it is in this condition that the probability of a successful launch is increased, and a virtuous closed-loop commercial satellite launch market is promoted. 
Finally, this results in a win-win situation in the supply chain. 
However, it is worth noting that when the government provides subsidies to blockchain technology embedded launch activities, it will maximize the funds' effectiveness, achieving all-win among the satellite operator, the vehicle manufacturer, and customers.


\subsection{ Future research}
For the future studies, we suggest several probable future directions.
First, the risk attitude of different participants can be taken into account which will effect the optimal decisions.
Second, the JIT operation management with the supported of blockchain in launch supply chain can be promising directions for future research.
Last but not least, multi-tier supply chain or supply chain network will be interesting to investigate, which involve more members such as the rideshare broker in piggyback launch and rideshare or cluster launch \citep{Barschke2020}. 









%	A table containing numbers is more complex. \reftab{tab:result} shows how to add a wide table with different alignments. It is suggested that use an Excel plugin ``Excel2LaTeX.xla'' to create a data table.
%	\begin{table*}[htbp]
%		\scriptsize
%%		\hspace*{-1cm} % apply this to move the table left, so that the right part of a wide table can be shown.
%		\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
%		\caption{\label{tab:result} Experimental results for the data sets \textit{Random} and \textit{Circles}.}
%		\centering
%		\renewcommand{\arraystretch}{1.3}
%		\begin{tabular}{@{\extracolsep{2pt}}l*{14}{r}@{}}		
%			\toprule
%			\multirow{2}*{Index}
%			& \multicolumn{7}{c}{Random}
%			& \multicolumn{7}{c}{Circles}\\
%			\cline{2-8}\cline{9-15}
%			& \multicolumn{1}{c}{20} & \multicolumn{1}{c}{60} & \multicolumn{1}{c}{100} & \multicolumn{1}{c}{200} & \multicolumn{1}{c}{300} & \multicolumn{1}{c}{400} & \multicolumn{1}{c}{500} & \multicolumn{1}{c}{20} & \multicolumn{1}{c}{60} & \multicolumn{1}{c}{100} & \multicolumn{1}{c}{200} & \multicolumn{1}{c}{300} & \multicolumn{1}{c}{400} & \multicolumn{1}{c}{500}\\
%			\midrule
%			$z_1$ & 0.85 & 0.6 & 0.53 & 0.44 & 0.41 & 0.42 & 0.41 & 0.6 & 0.45 & 0.43 & 0.41 & 0.39 & 0.4 & 0.38\\
%			$z_2$ & 0.85 & 0.46 & 0.51 & 0.4 & 0.39 & 0.4 & 0.37 & 0.45 & 0.42 & 0.38 & 0.38 & 0.37 & 0.37 & 0.37\\
%			\bottomrule			
%		\end{tabular}
%	\end{table*}
%	
%	\section{Math}
%	In-text equations like $a_{ij,t} \sim N(75, 25^2)$. For multiple equations, use \textit{eqnarray} and \& to align.
%	\begin{equation}\label{equ:utility} 	
%		U_{ij,t} = \left(\frac{W^{min}_{i,t}}{W_{ij,t}} \right)^{1-\beta}\cdot \left( \frac{Q_{j,t}}{Q^{max}_{t}} \right) ^{\beta},
%	\end{equation}
%	where
%	\begin{eqnarray}
%		\label{equ:maxtau} W^{\min}_{i,t}&=&\min \{W_{ij,t}\}^N_{j=1}, \\
%		\label{equ:minfq} Q^{\max}_{t}&=&\max \{Q_{j,t}\}^N_{j=1}.
%	\end{eqnarray}\par
%	\begin{eqnarray}\label{eq:B5}	
%		\left\{
%		\begin{aligned}
%		&\frac{\partial \pi_1}{\partial p_1}
%		= \dfrac{Qe^{b-ap_1}}{\displaystyle \sum_{f\in \mathcal{F}} e^{b-a p_f}} 
%		+ \dfrac{a(c_1-p_1)Qe^{b-ap_1}}{\displaystyle \sum_{f\in \mathcal{F}} e^{b-a p_f}} 
%		- \dfrac{a(c_1-p_1)Qe^{2(b-ap_1)}}{\big(\displaystyle \sum_{f\in \mathcal{F}} e^{b-a p_f}\big)^2} = 0,\\
%		&\dots,\\
%		&\frac{\partial \pi_n}{\partial p_n}
%		= \dfrac{Qe^{b-ap_n}}{\displaystyle \sum_{f\in \mathcal{F}} e^{b-a p_f}} 
%		+ \dfrac{a(c_n-p_n)Qe^{b-ap_n}}{\displaystyle \sum_{f\in \mathcal{F}} e^{b-a p_f}} 
%		- \dfrac{a(c_n-p_n)Qe^{2(b-ap_n)}}{\big(\displaystyle \sum_{f\in \mathcal{F}} e^{b-a p_f}\big)^2} = 0.
%		\end{aligned}
%		\right.
%	\end{eqnarray}
%	\begin{equation}\label{equ:if} 	
%	  f(x)= 
%	  \begin{cases}
%			\frac{x^2-x}{x},& \text{if } x\geq 1\\
%			0,             & \text{otherwise}
%		\end{cases}
%	\end{equation}
%	
%	\section{Citation}
%	Use \textbackslash{citet} when the authors are the subject of a sentence; otherwise use \textbackslash{citep}. For example, \citet{1929-Hotelling-p41-57} has spurred voluminous subsequent research on this topic... The term O2O originally means that the customer enjoys the product or service offline through buying online \citep{2010-Rampell-p-}. By means of agent-based modelling (ABM), the CAS theory can be applied to study various complex systems such as ecosystems, supply networks, financial markets, economies, and social systems \citep[see, e.g., ][]{2009-Farmer-p685-686, 2016-Chandrasekaran-p390-416}.\par
%	
%		
%	\section{Conclusion}\label{sec:conclusion}
%	The conclusion goes here.\par
%	
%	
%	\section*{Acknowledgement}
%	Dong was supported in part by the National Natural Science Foundation of China (No. 71573244, 71532013, 71202115 and 71403260). The authors acknowledge Mr. XXX for providing useful data and suggestions. The authors greatly appreciate the editor and anonymous referees for their comments, which helped to improve this paper.
%	
%	\appendix
%	\section{Pseudo Codes}\label{sec:apd:code}
%	\subsection{The procedure}
%	Algorithm \refalg{alg:CIPS} shows a piece of pseudo code.\par
%	\begin{figure}%[!t]
%		%		\removelatexerror
%		\begin{algorithm}[H]
%			\caption{The CIPS generation procedure}\label{alg:CIPS}
%			\KwData{A set $Y$ containing $n$ demand points with ($x$, $y$) coordinates and coverage radius $R$.}
%			\KwResult{A set $C$ consisting of intersection points and demand points with their coordinates.}
%			%			initialize population $P = \left \{ X_{1}, ... , X_{N} \right \} $\;
%			Create a temporary set copied from $Y$\;
%			\For( \emph{loop $Y$}){$i$ in range($n$)}
%			{
%				\For( \emph{loop $Y$}){$j$ in range($n$)}
%				{
%					$d_{i,j} =$ distance between $Y_i$ and $Y_j$\;
%					\If{$0 < d_{i,j}\leq2R$ }
%					{
%						Calculate the coordinates of intersection points\;
%						Add generated IPs to the temporary set\;
%					}					
%				}
%			}
%			Return the temporary set as $C$\;
%		\end{algorithm}
%	\end{figure}
%
%	\newpage
%%	\section*{References}
	\bibliographystyle{model5-names-with-volume-number}
%	\bibliographystyle{IEEEtran}
%\bibliographystyle{ACM-Reference-Format}
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