5. [Subgame perfection] Consider the following game. Two friends, Anne (A) and Bob (B), are trying to coordinate on a joint activity, which can be either knitting (K) or fencing (F). Both friends prefer coordinating (i.e., choosing the same activity) to not coordinating but, conditional on coordinating, A prefers K to F while B prefers F to K. In the game, A chooses K or F first; B observes A's choice and then chooses K or F himself. 3

a. Draw a game tree that depicts the game above. Assign numerical payoffs that capture the preferences described. I suggest setting the miscoordination payoffs for both A and B to zero, but this is not necessary.

b. Is there a Nash equilibrium in which the players coordinate on fencing? If so, describe the two players' strategies. If not, explain why not.

c. Is there a subgame perfect Nash equilibrium in which the players coordinate on fencing? If so, describe the two players' strategies. If not, explain why not.

d. List all possible outcomes of the game if play is according to a subgame perfect equilibrium.