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Problem 1: Game theory.
Siskel and Ebert would both like to see Casablanca. Players simultaneously chose theater to see the movie Uptown or Downtown. Each movie ticket costs $10. If Siskel and Elbert choose different movie theaters, they each get a value of $10. If both chose Uptown, they each get a value of $20. If both choose Downtown, they each get a value of $30.
a) Fill in the following payoff matrix
b) Find all four best responses of this game
c) What are the Nash equilibria of this game?
d) Design the payoff matrix of a game with no Nash equilibria. The game should have two players, two strategies for each player, and the payoffs for each player should be either 0 or 1.
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