Problem
Consider the following variant of the Battle of the Sexes. Chris and Pat are deciding which concert to go to. They can either go listen to Britney or Swift (both great options).
1. Find all pure strategy Nash Equilibria of this game.
2. If each player played each strategy randomly, what is the overall probability that they coordinate on a show? That is, what is the overall probability that (Britney,Britney) or (Swift,Swift) arises?
3. When this game is actually played in the laboratory, Player 1 chooses Swift about 3 4 of the time, whereas Player 2 chooses Britney about 3 4 of the time. What is the probability that the two actually coordinate? Is this better or worse than if they were each playing random strategies?
4. Using the level-k model, explain what a level-0, level-1, level-2, level-3, and level-4 Chris would do. Explain what a level-0, level-1, level-2, level-3, and level-4 Pat would do.
5. If you wanted to use the level-k model to explain the the mis-coordination between players, what level would each player have to be?