Benchmark 
the basic payoff function

Profits:=-α p+e(F-(1-α)p)-cs

Profitv:=α p+e (1-α)p-(1-e)θ-k*(e*e)-cv
Profitc:=Profitv+Profits

Profitc

Simplify[-cs-cv-(e^2) k+e (F-p (1-α))+e p (1-α)-(1-e) θ]

the constraints

Solve[%==0,e]

The optimal of e

the first derivative

D[Profitc,e]

Solve[F-2 e k+θ==0,e]

e:=%

e:=((F+θ)/(2 k))

e

the maximum profit of the centre supply chain at the optimal e

Profitc

Simplify[-cs-cv+(((F-p (1-α)) (F+θ))/(2 k))+((p (1-α) (F+θ))/(2 k))-((((F+θ))^2)/(4 k))-θ (1-((F+θ)/(2 k)))]

(((F^2)-4 cs k-4 cv k+2 F θ-4 k θ+(θ^2))/(4 k))
Profitv:=α p+e (1-α)p-(1-e)θ-k*(e*e)-cv

the maximum profit of the vehicle manufacture at that e

The insurance model (satellite owner buy the insurance contract from the third party)

the vehicle manufacture

he decide the optimal e

D[Profitv,e]

-2 e k+p (1-α)+θ
Solve[-2 e k+p (1-α)+θ==0,e]

e:=((p-p α+θ)/(2 k))

the maximum profit of vehicle manufacture

Profitv

Simplify[-cv+p α+((p (1-α) (p-p α+θ))/(2 k))-((((p-p α+θ))^2)/(4 k))-θ (1-((p-p α+θ)/(2 k)))]

((-4 cv k+(p^2) (((-1+α))^2)+θ (-4 k+θ)+2 p (2 k α+θ-α θ))/(4 k))

Profits:=-α p+e(F-(1-α)p)-cs

the satellite owner

Profits

Simplify[-cs-p α+(((F-p (1-α)) (p-p α+θ))/(2 k))]

Profitcc=Profits+Profitv

Simplify[Profitcc]

D[Profits,α]

Simplify[-p-((p (F-p (1-α)))/(2 k))+((p (p-p α+θ))/(2 k))]

Solve[-((p (F+2 k-2 p+2 p α-θ))/(2 k))==0,α]

2⃣️   If the satellite owner buy insurance contract from the third party ( insurance company)

Profitv:=α p+e (1-α)p-(1-e)θ-k*(e*e)-cv
Profits:=-α p+e(F-(1-α) )p-cs-(1+ri)p+(1-e)(α p+cs )

e:=((p-p α+θ)/(2 k))

Profits

Simplify[-cs-p (1+ri)-p α+((p (-1+F+α) (p-p α+θ))/(2 k))+(cs+p α) (1-((p-p α+θ)/(2 k)))]

Simplify[-cs-p (1+ri)-p α+((p (-1+F+α) (p-p α+θ))/(2 k))+(cs+p α) (1-((p-p α+θ)/(2 k)))]

D[-cs-p (1+ri)-p α+((p (-1+F+α) (p-p α+θ))/(2 k))+(cs+p α) (1-((p-p α+θ)/(2 k))),α]

Simplify[-p-(((p^2) (-1+F+α))/(2 k))+((p (cs+p α))/(2 k))+((p (p-p α+θ))/(2 k))+p (1-((p-p α+θ)/(2 k)))]

D[-cs-p (1+ri)-p α+((p (-1+F+α) (p-p α+θ))/(2 k))+(cs+p α) (1-((p-p α+θ)/(2 k))),p]

Simplify[-1-ri-α+((p (1-α) (-1+F+α))/(2 k))-(((1-α) (cs+p α))/(2 k))+(((-1+F+α) (p-p α+θ))/(2 k))+α (1-((p-p α+θ)/(2 k)))]

Solve[((-2 k (1+ri)+cs (-1+α)-(-1+F) (2 p (-1+α)-θ))/(2 k))==0,p]

{{p->((-cs-2 k-2 k ri+cs α-θ+F θ)/(2 (-1+F) (-1+α)))}}
p:=((-cs-2 k-2 k ri+cs α-θ+F θ)/(2 (-1+F) (-1+α)))

Profits

Simplify[%18]