Kamiński Dominik, Miekisz Jacek, Zaborowski Marcin
Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland.
Bull Math Biol. 2005 Nov;67(6):1195-205. doi: 10.1016/j.bulm.2005.01.004.
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.
动物行为和进化通常可用博弈论模型来描述。尽管在许多情况下参与者数量非常多，但它们的策略互动通常可分解为一系列两人博弈。直到最近，才为多人博弈定义了进化稳定策略并分析了其性质[布鲁姆，M.，坎宁斯，C.，维克斯，G.T.，1997年。多人矩阵博弈。数学生物学通报59，931 - 952]。在此，我们研究参与对称三人博弈的随机匹配个体群体的随机动态的长期行为。我们分析具有多个进化稳定策略的博弈中均衡的随机稳定性。我们还表明，在某些博弈中，一个群体从长远来看可能不会进化到进化稳定均衡。
