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Stochastic stability in three-player games

Bulletin of Mathematical Biology volume 67, pages 1195–1205 (2005)Cite this article

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 were evolutionarily stable strategies defined for multi-player games and their properties analyzed [Broom, M., Cannings, C., Vickers, G.T., 1997. Multi-player matrix games. Bull. Math. Biol. 59, 931–952]. Here we study the long-run behavior of stochastic dynamics of populations of randomly matched individuals playing symmetric three-player games. We analyze the 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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Affiliations

  1. Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Dominik Kamiński, Jacek Miekisz & Marcin Zaborowski

Authors
  1. Dominik Kamiński
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  2. Jacek Miekisz
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  3. Marcin Zaborowski
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Kamiński, D., Miekisz, J. & Zaborowski, M. Stochastic stability in three-player games. Bull. Math. Biol. 67, 1195–1205 (2005). https://doi.org/10.1016/j.bulm.2005.01.004

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  • DOI: https://doi.org/10.1016/j.bulm.2005.01.004

Keywords

  • Nash Equilibrium
  • Payoff
  • Evolutionary Game
  • Stable Strategy
  • Tree Representation