# PS3 Solution - Kaushik Basu Fall 2009 Econ 367...

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Kaushik Basu Fall 2009 Econ 367 Game-Theoretic Methods Problem Set 3 Solutions 1. Consider a two-player game in which each of two players (A and B) has to choose a positive integer, and they receive payoffs as follows. If both choose 1, they get 1 dollar each. If one player chooses 1 and the other something else, they get 0 each. Now consider only integers 2 or greater: If one player chooses an integer t and the other chooses the integer t+1, the former gets 2 dollars and the latter gets 3 dollars. For all other choices they get 2 dollars each. Draw a ‘partial’ payoff matrix of the above game by showing what would happen up to integer 4. That is, show the part of the game where each person’s strategy is restricted to the integers 1, 2, 3, 4. Answer: The only Nash equilibrium of this game is (1,1). (That is, each player plays 1) Is there a non-Nash behavior that seems as or more reasonable than behavior consistent with Nash. (Confine your answer to no more than 2 or 3 sentences.)

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## This note was uploaded on 10/03/2009 for the course ECON 3670 taught by Professor Basu during the Fall '08 term at Cornell University (Engineering School).

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PS3 Solution - Kaushik Basu Fall 2009 Econ 367...

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