Bart and Lisa are playing a game of Rock-Paper- Scissors. They hold their hands behind their backs and on the count of 3 show whether they are playing rock, paper, or scissors. When she makes her choice, Lisa doesnt know what Bart is going to do. Before he decides what to do, Bart peeks behind Lisas back. If Lisa is going to play scissors, Bart can tell by looking that she will play scissors. If she is going to play rock or paper, Bart cant tell which of these she will do. The payoff in this game are the same as in ordinary Rock-Paper-Scissors. The winner gets a payoff of 1, the loser gets -1. Rock beats scissors, scissors beats paper, paper beats rock. If both players show the same thing, both get 0. Lisa knows that Bart peeks and she knows that he can tell if she is going to do scissors, but when she isnt going to do scissors, he cant tell whether she will do paper or rock.

A) Show this game in extensive form.

B) How many strategies are possible for Lisa? How many strategies are possible for Bart?

C) Show this game in strategic form.

D) Which if any of the possible strategies for Bart are weakly dominated? If Lisa believes that Bart will not use weakly dominated strategies, are there any strategies that she will not use? Explain

E) If Bart knows that Lisa knows that Bart is rational, what strategies will he not use. F) Find a mixed strategy Nash equilibrium for this game. In equilibrium, what are the expected payos for Bart? for Lisa