GAME THEORY

Problem 1. Consider a slight modication of the Model of entry game from our lectures. Again, there are two rms, A (a potential entrant) and B (an incumbent monopolist), involved in a game where A moves rst. A either stays out, in which case A gets 2 and B gets 3, or enters B 's market. If A enters, the rms simultaneously choose between two actions: Hawk (an aggro-live action) and Dove (a peaceful action). The payoffs in this subgame are as follows: (i) if a rm chooses Hawk and the other plays Dove, then Hawk gets 3 and Dove gets 0; (ii) if both play Hawk, then each gets 1; (iii) if both choose Dove, then each gets 1. For task (a) below, use the bimatrixgame representation of the game by rst listing the players' strategies. For (b), use backde induction. In the lectures, we only covered sequential games with perfect information, which is not the case here, as the rms decide simultaneously in the second stage of the game (after A enters). But backward induction is analogous here: rst solve for the NE in the second-stage subgame, then use these NE results to conclude about A's decision on whether or not to enter. a) Find all Nash equilibria of the game. Show your work. 5 points b) Find all subgameperfect Nash equilibria of the game. Show your work. 5 points