The number of pure Nash equilibria in a random game with nondecreasing best responses |
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Authors: | Satoru Takahashi |
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Affiliation: | aDepartment of Economics, Princeton University, Princeton, NJ 08544-1021, USA |
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Abstract: | We randomly draw a game from a distribution on the set of two-player games with a given size. We compute the distribution and the expectation of the number of pure-strategy Nash equilibria of the game conditional on the game having nondecreasing best-response functions. The conditional expected number of pure-strategy Nash equilibria becomes much larger than the unconditional expected number as the size of the game grows. |
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Keywords: | Number of Nash equilibria Random game Strategic complementarity Increasing difference Single crossing |
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