(Solved): Firm 1 And Firm 2 Are Competing For Franchise. The Present Value Of The Net Revenues Generated By T...

Firm 1 and firm 2 are competing for franchise. The present value of the net revenues generated by the franchise are equal to 11. Each firm’s probability of winning the franchise is given by its proportion of the total spent by the two firms on lobbying the local government committee that awards the franchise. That is, if I₁ and I₂ represent the lobbying expenditures of firms 1 and 2, respectively, then firm 1’s probability of winning is given by I₁/(I₁ + I₂), while firm 2’s probability of winning is I₂/(I₁ + I₂). If each firm assumes that the other firm’s spending is independent of its own, what is the equilibrium level of spending for each firm?

Equilibrium for firm 1:

Equilibrium for firm 2: