One day, Sam and Ryan play odds/evens to see who gets the last doughnut. On command, they each extend one or two fingers. If the sum is odd Sam wins the doughnut, if the sum is even Ryan wins the doughnut. Suppose the payoff from winning the doughnut is 1 and the payoff from losing is 0. a) Illustrate this interaction as a game in matrix form. b) Suppose that Sam thinks that Ryan will play one finger for sure? What will Sam play? Does Sam have reason to think that Ryan will play one finger for sure? c) Do either of them have a strictly dominated strategy? d) Find the pure strategy Nash equilibria of the game, if any.
One day, Sam and Ryan play odds/evens to see who gets the last doughnut. On command, they each extend one or two fingers. If the sum is odd Sam wins the doughnut, if the sum is even Ryan wins the doughnut. Suppose the payoff from winning the doughnut is 1 and the payoff from losing is 0. a) Illustrate this interaction as a game in matrix form. b) Suppose that Sam thinks that Ryan will play one finger for sure? What will Sam play? Does Sam have reason to think that Ryan will play one finger for sure? c) Do either of them have a strictly dominated strategy? d) Find the pure strategy Nash equilibria of the game, if any.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.5P
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Question
H2.
One day, Sam and Ryan play odds/evens to see who gets the last doughnut. On command, they each extend one or two fingers. If the sum is odd Sam wins the doughnut, if the sum is even Ryan wins the doughnut. Suppose the payoff from winning the doughnut is 1 and the payoff from losing is 0.
a) Illustrate this interaction as a game in matrix form.
b) Suppose that Sam thinks that Ryan will play one finger for sure? What will Sam play? Does Sam have reason to think that Ryan will play one finger for sure?
c) Do either of them have a strictly dominated strategy?
d) Find the pure strategy Nash equilibria of the game, if any.
e) Suppose that Sam thinks that Ryan will play one finger or two fingers with even odds. Will Ryan play one finger for sure, play two fingers for
sure or play each strategy with even odds? Does Sam have good reason to believe that Ryan will play one finger or two fingers with even odds?
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