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 doesn’t know what Bart is going to do. Before he decides what to do, Bart peeks behind Lisa’s 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 can’t tell which of these she will do. The payoffs 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 isn’t going to do scissors, he can’t 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.