Econ 367 PS3 - Kaushik Basu Spring 2008 Econ 367...

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Kaushik Basu Spring 2008 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. Locate all the Nash equilibria of this game. 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.) Answer: (a) Unique Nash Equilibrium: (1,1) (b) Playing anything other than 1 will give both the players strictly more pay-off and thus they can ensure that they can get at least 2 dollars each.
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