Econ 402, Penn State Univesity , strategy, Ron Siegel

1. (40 points) Two friends, player 1 and 2, are contemplating whether to go out. Player 1 rst decides whether he would like to go out and noties player 2 of his decision. If player 1 goes out, then player 2 decides whether to join him. If she does, they each get a payoff of 2. If she does not, they each get a payoff of 1. If player 1 does not go out, player 2 decides whether to go out by herself. If she does, her payoff is 4. If she does not, her payo is 5. Player 1's payoif from not going out is 0. (a) (5 points) Draw the extensive form of this game, labeling all parts. (b) (5 points) Depict the normal form of this game as a matrix. Suppose that b = 5. (c) (5 points) If all you know is that the players are rational, what can you say about the strategies they will choose and the payoffs they will obtain? (d) (5 points) If you also assume that rationality is common knowledge, what can you say about the strategies they will choose and the payoffs they will obtain? (e) (5 points) What are the Nash equilibria? Suppose that b = 3. (f) (5 points) If all you know is that the players are rational, what can you say about the strategies they will choose and the payoffs they will obtain? (g) (5 points) If you also assume that rationality is common knowledge, what can you say about the strategies they will choose and the payoffs they will obtain? (h) (5 points) What are the Nash equilibria