4. Firm 1 chooses to enter a market or not, and if 1 enters, then firm 2 (an incumbent firm) chooses to fight or not fight. If firm 1 does not enter then it earns 0 and firm 2 earns 10. If firm 1 enters and firm 2 does not fight, then each firm earns 5 . If firm 1 enters and firm 2 fights, then each earns 1. Before firms 1 chooses to enter, firm 2 has a choice of adding production capacity. Adding capacity costs 4 regardless of what follows. However, if firm 2 does have the added capacity then if it fights firm 1, it would earn 10 (not accounting for added capacity costs) while firm 1 would still earn 1. The game has perfect information: firm 1 observes if firm 2 adds capacity or not and then chooses to enter or not, and firm 2 observes firm 1 's entry decision and chooses to fight or not when 1 enters. a. Draw the extensive form (including labeling the payoffs associated with each terminal node, firm 1's payoff first). b. Find a subgame perfect equilibrium of the game (specifying behavior at each node). c. Find a Nash equilibrium of the game that is not subgame perfect (specifying behavior at each node). 4. Firm 1 chooses to enter a market or not, and if 1 enters, then firm 2 (an incumbent firm) chooses to fight or not fight. If firm 1 does not enter then it earns 0 and firm 2 earns 10. If firm 1 enters and firm 2 does not fight, then each firm earns 5 . If firm 1 enters and firm 2 fights, then each earns 1. Before firms 1 chooses to enter, firm 2 has a choice of adding production capacity. Adding capacity costs 4 regardless of what follows. However, if firm 2 does have the added capacity then if it fights firm 1, it would earn 10 (not accounting for added capacity costs) while firm 1 would still earn 1. The game has perfect information: firm 1 observes if firm 2 adds capacity or not and then chooses to enter or not, and firm 2 observes firm 1 's entry decision and chooses to fight or not when 1 enters. a. Draw the extensive form (including labeling the payoffs associated with each terminal node, firm 1's payoff first). b. Find a subgame perfect equilibrium of the game (specifying behavior at each node). c. Find a Nash equilibrium of the game that is not subgame perfect (specifying behavior at each node)
