A theorem on the number of Nash equilibria in a bimatrix game

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Abstract

We show that if y is an odd integer between 1 and 2″ - 1, there is an n × n bimatrix game with exactly y Nash equilibria (NE). We conjecture that this 2″ - 1 is a tight upper bound on the number of NEs in a "nondegenerate" n × n game.

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Quint, T., & Shubik, M. (1997). A theorem on the number of Nash equilibria in a bimatrix game. International Journal of Game Theory, 26(3), 353–359. https://doi.org/10.1007/BF01263276

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