Problem 2. Nash Equilibria in a simple game (19 points) Two firms are deciding simultaneously whether to enter a market. If neither enters, they make zero pofits. If both enters, they make profits -1, since the market is too small for two firms. If only one enters, that firm makes high profits. This game is summarized in the following matrix: 1 \\ 2 Enter Do not Enter Enter -2, -1 10, 0 Do not Enter 0, 5 0, 0 1. What are the pure-strategy Nash Equilibria of this game? (3 points) 2. Now assume that firm 1 can enter the market with probability p, and firm 2 can enter the market with probability p2. Write down the expected utlity of each firm as a function of the strategy of the other player, and find the best response correspondence for firms 1 and 2. (8 points) 3. Graph these best response correspondences and find the Nash equilibria in mixed strategies. (5 points) 4. Is there one equilibrium out of these that seems more plausible to you? (3 points)