Blockchain Model--VM leader
The SO's Effort Under Insurance Model

Profitsb:=-α pb+eb(f-(1-α)pb)-cs -rb(α pb+cs+f)+(1-eb)(α pb+cs+f)-csb
Profitib:=rb(α pb+cs+f)-(1-eb)(α pb+cs+f)
Profitvb:=α pb+eb (1-α)pb-(1-eb)θ-kb*(eb*eb)-cv-cvb

we assume the SA , to simplfy the question, we set the α=1- β*pb, then the payoff of SA is :

Profitsb2:=-(1-β pb) pb+eb (f-(1-(1-β pb ))pb)-cs -rb((1-β pb )pb+cs+f)+(1-eb )((1-β pb ) pb+cs+f)-csb

D[Profitsb2,pb]

Solve[%==0,pb]

The IC's Premium Rate

Profitib:=rb((1-β pb ) pb+cs+f)-(1-eb)((1-β pb ) pb+cs+f)
pb:=((eb+rb)/(2 rb β))

Solve[Profitib==0,rb]

The VM's Optimal Decision

pb:=((eb+rb)/(2 rb β))
rb:=1-eb
Profitvb:=(1-β pb ) pb+eb (1-(1-β pb ))pb-(1-eb)θ-kb*(eb*eb)-cv-cvb

Profitvb

Simplify[-cv-cvb-(eb^2) kb+((1-(1/(2 (1-eb))))/(2 (1-eb) β))+(eb/(4 (((1-eb))^2) β))-(1-eb) θ]

D[%,eb]

Solve[%==0,eb]