Stochastic stability in three-player games

Dominik Kaminski; Jacek Miekisz; Marcin Zaborowski

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Stochastic stability in three-player games

Dominik Kaminski·Jacek Miekisz·Marcin Zaborowski

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Abstract

Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only recently evolutionarily stable strategies were defined for multi-player games and their properties analyzed (Broom et al., 1997). Here we study the long-run behavior of stochastic dynamics of populations of randomly matched individuals playing symmetric three-player games. We analyze stochastic stability of equilibria in games with multiple evolutionarily stable strategies. We also show that in some games, a population may not evolve in the long run to an evolutionarily stable equilibrium.

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Dominik Kaminski, Jacek Miekisz, Marcin Zaborowski. 2004-12-22. Stochastic stability in three-player games. https://arxiv.org/abs/q-bio/0412041

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