Game theory

2. Two firms play the following game. Firm 1 chooses a quantity q1, and this is observed by Firm 2, who in turn chooses his quantity q2. The inverse demand function is P(q1 + q2) = 5 – (q1 + q2) and both firms’ marginal cost is 1. Firms’ profit at the end of the game is their revenue minus their cost. (a) Find the quantities produced in a Subgame Perfect Nash Equilibrium and each firm’s profit. (b) How much would Firm 2 be willing to pay to change the order of play and become the first one to move? 

1.  Consider the following extensive form game (attached): (a) Give the normal form representation of this game. (b) Find all pure strategy Nash equilibria. (c) Using Backward Induction, find the Subgame Perfect Nash Equilibrium of this game.