Stochastic evolutionary dynamics of bimatrix games |
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Authors: | Hisashi Ohtsuki |
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Institution: | a PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan b Department of Value and Decision Science, Tokyo Institute of Technology, 2-12-1-W9-35 O-okayama, Meguro, Tokyo 152-8552, Japan |
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Abstract: | Evolutionary game dynamics of two-player asymmetric games in finite populations is studied. We consider two roles in the game, roles α and β. α-players and β-players interact and gain payoffs. The game is described by a pair of matrices, which is called bimatrix. One's payoff in the game is interpreted as its fecundity, thus strategies are subject to natural selection. In addition, strategies can randomly mutate to others. We formulate a stochastic evolutionary game dynamics of bimatrix games as a frequency-dependent Moran process with mutation. We analytically derive the stationary distribution of strategies under weak selection. Our result provides a criterion for equilibrium selection in general bimatrix games. |
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Keywords: | Evolutionary game theory Finite population Stochastic evolution |
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