Schaffer M E
Department of Economics, London School of Economics, England.
J Theor Biol. 1988 Jun 22;132(4):469-78. doi: 10.1016/s0022-5193(88)80085-7.
This paper presents a generalization of Maynard Smith's concept of an evolutionarily stable strategy (ESS) to cover the cases of a finite population and a variable contest size. Both equilibrium and stability conditions are analysed. The standard Maynard Smith ESS with an infinite population and a contest size of two (pairwise contests) is shown to be a special case of this generalized ESS. An important implication of the generalized ESS is that in finite populations the behaviour of an ESS player is "spiteful", in the sense that an ESS player acts not only to increase his payoff but also to decrease the payoffs of his competitors. The degree of this "spiteful" behaviour is shown to increase with a decrease in the population size, and so is most likely to be observed in small populations. The paper concludes with an extended example: a symmetric two-pure-strategies two-player game for a finite population. It is shown that a mixed strategy ESS is globally stable against invasion by any one type of mutant strategist. The condition for the start of simultaneous invasion by two types of mutant is also given.
本文对梅纳德·史密斯的进化稳定策略（ESS）概念进行了推广，以涵盖有限种群和可变竞争规模的情况。对均衡条件和稳定性条件都进行了分析。具有无限种群和规模为二的竞争（成对竞争）的标准梅纳德·史密斯ESS被证明是这种广义ESS的一个特殊情况。广义ESS的一个重要含义是，在有限种群中，ESS参与者的行为是“恶意的”，从这个意义上说，ESS参与者不仅采取行动增加自己的收益，还会降低其竞争对手的收益。这种“恶意”行为的程度随着种群规模的减小而增加，因此最有可能在小种群中观察到。本文最后给出了一个扩展示例：一个针对有限种群的对称双纯策略两人博弈。结果表明，混合策略ESS对任何一种类型的突变策略家的入侵都是全局稳定的。还给出了两种类型的突变同时开始入侵的条件。
