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An ESS is a [[solution concept|refined]] or modified form of a [[Nash equilibrium]]. (See the next section for examples which contrast the two.) In a Nash equilibrium, if all players adopt their respective parts, no player can ''benefit'' by switching to any alternative strategy. In a two player game, it is a strategy pair. Let E(''S'',''T'') represent the payoff for playing strategy ''S'' against strategy ''T''.  The strategy pair (''S'', ''S'') is a Nash equilibrium in a two player game if and only if this is true for both players and for all ''T''≠''S'':

An ESS is a [[solution concept|refined]] or modified form of a [[Nash equilibrium]]. (See the next section for examples which contrast the two.) In a Nash equilibrium, if all players adopt their respective parts, no player can ''benefit'' by switching to any alternative strategy. In a two player game, it is a strategy pair. Let E(''S'',''T'') represent the payoff for playing strategy ''S'' against strategy ''T''.  The strategy pair (''S'', ''S'') is a Nash equilibrium in a two player game if and only if this is true for both players and for all ''T''≠''S'':

An ESS is a refined or modified form of a Nash equilibrium. (See the next section for examples which contrast the two.) In a Nash equilibrium, if all players adopt their respective parts, no player can benefit by switching to any alternative strategy. In a two player game, it is a strategy pair. Let E(S,T) represent the payoff for playing strategy S against strategy T.  The strategy pair (S, S) is a Nash equilibrium in a two player game if and only if this is true for both players and for all T≠S:

An ESS is a refined or modified form of a Nash equilibrium. (See the next section for examples which contrast the two.) In a Nash equilibrium, if all players adopt their respective parts, no player can benefit by switching to any alternative strategy. In a two player game, it is a strategy pair. Let E(S,T) represent the payoff for playing strategy S against strategy T.  The strategy pair (S, S) is a Nash equilibrium in a two player game if and only if this is true for both players and for all T≠S:

[[John Maynard Smith|Maynard Smith]] and [[George R. Price|Price]]<ref name="JMSandP73"/> specify two conditions for a strategy ''S'' to be an ESS.  For all ''T''≠''S'', either

[[John Maynard Smith|Maynard Smith]] and [[George R. Price|Price]]<ref name="JMSandP73"/> specify two conditions for a strategy ''S'' to be an ESS.  For all ''T''≠''S'', either

Maynard Smith and Price specify two conditions for a strategy S to be an ESS.  For all T≠S, either

Maynard Smith and Price specify two conditions for a strategy S to be an ESS.  For all T≠S, either

梅纳德·史密斯和普莱斯为策略S指定了两个条件，使其成为进化均衡策略，对于所有的T≠S，两个选其一：

梅纳德·史密斯和普莱斯为策略S指定了两个条件，使其成为进化均衡策略，对于所有的T≠S，两个选其一：

1. E(S,S) > E(T,S), or

1. E(S,S) > E(T,S), 或者

2. E(S,S) = E(T,S) and E(S,T) > E(T,T)

2. E(S,S) = E(T,S) and E(S,T) > E(T,T)

There is also an alternative, stronger definition of ESS, due to Thomas.<ref name="Thomas85">{{cite journal |author=Thomas, B. |title=On evolutionarily stable sets |journal=J. Math. Biology |volume=22 |pages=105–115 |year=1985 |doi=10.1007/bf00276549}}</ref>  This places a different emphasis on the role of the Nash equilibrium concept in the ESS concept.  Following the terminology given in the first definition above, this definition requires that for all ''T''≠''S''

There is also an alternative, stronger definition of ESS, due to Thomas.<ref name="Thomas85">{{cite journal |author=Thomas, B. |title=On evolutionarily stable sets |journal=J. Math. Biology |volume=22 |pages=105–115 |year=1985 |doi=10.1007/bf00276549}}</ref>  This places a different emphasis on the role of the Nash equilibrium concept in the ESS concept.  Following the terminology given in the first definition above, this definition requires that for all ''T''≠''S''

There is also an alternative, stronger definition of ESS, due to Thomas.  This places a different emphasis on the role of the Nash equilibrium concept in the ESS concept.  Following the terminology given in the first definition above, this definition requires that for all T≠S

There is also an alternative, stronger definition of ESS, due to Thomas.  This places a different emphasis on the role of the Nash equilibrium concept in the ESS concept.  Following the terminology given in the first definition above, this definition requires that for all T≠S

后来伯恩哈德·托马斯Bernhard Thomas在他的论文《On evolutionarily stable sets》中提出了更大胆的定义。它不同于纳什平衡概念在进化均衡策略中的作用。根据上面第一个定义中给出的术语，此处要求对所有T≠S：

后来伯恩哈德·托马斯Bernhard Thomas在他的论文《On evolutionarily stable sets》中提出了更大胆的定义。它不同于纳什平衡概念在进化均衡策略中的作用。根据上面第一个定义中给出的术语，此处要求对所有T≠S：