You may discuss each problem with one or two other persons. Each person must do her or his own write
up. Moreover, you may not simply write down a solution and give it to the other person. You may present
things to each other on (say) a whiteboard, but the other person should not simply be copying things
over. You should acknowledge everyone you worked with, as well as all other sources, on the write up.
Assignments are always due immediately at the beginning of class.
1. Penalty Shots Revisited. Player 1 has to take a soccer penalty shot to decide the game. She can shoot
Left, Middle, or Right. Player 2 is the goalie. He can dive to the left, middle, or right. Actions are chosen
simultaneously. The payoffs are as follows.
(a) For each player, is any strategy dominated by another (pure) strategy?
(b) For what beliefs about player 1's strategy is m a best response for player 2? For what beliefs about
player 2's strategy is M a best response for player 1?
(c) Suppose player 2 puts himself in player 1's shoes and assumes that player 1, whatever is her belief,