进化稳定策略

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An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) which, if adopted by a population in a given environment, is impenetrable, meaning that it cannot be invaded by any alternative strategy (or strategies) that are initially rare. It is relevant in game theory, behavioural ecology, and evolutionary psychology. An ESS is an equilibrium refinement of the Nash equilibrium. It is a Nash equilibrium that is "evolutionarily" stable: once it is fixed in a population, natural selection alone is sufficient to prevent alternative (mutant) strategies from invading successfully. The theory is not intended to deal with the possibility of gross external changes to the environment that bring new selective forces to bear.

An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) which, if adopted by a population in a given environment, is impenetrable, meaning that it cannot be invaded by any alternative strategy (or strategies) that are initially rare. It is relevant in game theory, behavioural ecology, and evolutionary psychology. An ESS is an equilibrium refinement of the Nash equilibrium. It is a Nash equilibrium that is "evolutionarily" stable: once it is fixed in a population, natural selection alone is sufficient to prevent alternative (mutant) strategies from invading successfully. The theory is not intended to deal with the possibility of gross external changes to the environment that bring new selective forces to bear.

进化均衡策略Evolutionarily Stable Strategy（ESS）是指一个种群在特定环境下采用的策略或策略组，它具有不可渗透性，即该群体不可能被初期占比小的其他策略或策略组所入侵。它与博弈论，行为生态学和进化心理学有关。进化均衡策略ESS是纳什平衡Nash equilibrium（Q问题：在集智百科“博弈论”里面翻译为纳什平衡，在词条“Nash equilibrium”翻译为纳什均衡，暂时采用了博弈论里面的翻译）的细化，相当于是稳定进化的纳什平衡：一旦该种群采取了此策略，仅自然选择过程就足以防止其他（变异）的策略成功入侵。该理论并非旨在处理外部总体环境可能发生的变化，以此带来的全新的选择性力量。

First published as a specific term in the 1972 book by John Maynard Smith, the ESS is widely used in behavioural ecology and economics, and has been used in anthropology, evolutionary psychology, philosophy, and political science.

First published as a specific term in the 1972 book by John Maynard Smith, the ESS is widely used in behavioural ecology and economics, and has been used in anthropology, evolutionary psychology, philosophy, and political science.

在1972年由约翰·梅纳德·史密斯John Maynard Smith出版的书中，进化均衡策略ESS首次作为一个特定的术语出现，它广泛应用于行为生态学和经济学，同时在人类学、进化心理学、哲学和政治科学中均已被使用。

History 历史

Evolutionarily stable strategies were defined and introduced by John Maynard Smith and George R. Price in a 1973 Nature paper. Such was the time taken in peer-reviewing the paper for Nature that this was preceded by a 1972 essay by Maynard Smith in a book of essays titled On Evolution. The 1972 essay is sometimes cited instead of the 1973 paper, but university libraries are much more likely to have copies of Nature. Papers in Nature are usually short; in 1974, Maynard Smith published a longer paper in the Journal of Theoretical Biology. Maynard Smith explains further in his 1982 book Evolution and the Theory of Games. Sometimes these are cited instead. In fact, the ESS has become so central to game theory that often no citation is given, as the reader is assumed to be familiar with it.

Evolutionarily stable strategies were defined and introduced by John Maynard Smith and George R. Price in a 1973 Nature paper. Such was the time taken in peer-reviewing the paper for Nature that this was preceded by a 1972 essay by Maynard Smith in a book of essays titled On Evolution. （wiki后期添加的内容The 1972 essay is sometimes cited instead of the 1973 paper, but university libraries are much more likely to have copies of Nature. Papers in Nature are usually short; in 1974, Maynard Smith published a longer paper in the Journal of Theoretical Biology.[3] ）Maynard Smith explains further in his 1982 book Evolution and the Theory of Games. Sometimes these are cited instead. In fact, the ESS has become so central to game theory that often no citation is given, as the reader is assumed to be familiar with it.

进化均衡策略是由约翰·梅纳德·史密斯John Maynard Smith和 乔治·普赖斯George R. Price 在1973年的《自然》杂志上定义和提出的。但是由于同行评审《自然》的论文花费了大量时间，以至于在此之前，梅纳德 史密斯就在1972年的一本论文集《论进化论》中发表了另一篇论文。有时候学者们会选择引用1972年在《论进化论》上发表的论文而非1973年《自然》杂志上的，但大学图书馆可能收藏有《自然》的副本。通常《自然》杂志上的论文很短；随后1974年，梅纳德·史密斯在《理论生物学》杂志上又发表了一篇更长的论文。在1982年梅纳德·史密斯的新著作《演化与博弈论》中，他又进一步解释了这个概念。之后该版本的解释时常被引用。实际上，进化均衡策略已经成为了博弈论的核心，往往没有引证给出，因为假定了读者是熟悉它的。

Maynard Smith mathematically formalised a verbal argument made by Price, which he read while peer-reviewing Price's paper. When Maynard Smith realized that the somewhat disorganised Price was not ready to revise his article for publication, he offered to add Price as co-author.

Maynard Smith mathematically formalised a verbal argument made by Price, which he read while peer-reviewing Price's paper. When Maynard Smith realized that the somewhat disorganised Price was not ready to revise his article for publication, he offered to add Price as co-author.

当梅纳德·史密斯在同行评审普莱斯论文的时候读到了这个论点，随后他将这个口头论点数学形式化。之后史密斯意识到杂乱无章的普莱斯应该是还没有准备好修改他自己的文章去发表，于是就提出了加上普莱斯名字作为合著者。

The concept was derived from R. H. MacArthur and W. D. Hamilton's work on sex ratios, derived from Fisher's principle, especially Hamilton's (1967) concept of an unbeatable strategy. Maynard Smith was jointly awarded the 1999 Crafoord Prize for his development of the concept of evolutionarily stable strategies and the application of game theory to the evolution of behaviour.

The concept was derived from R. H. MacArthur and W. D. Hamilton's work on sex ratios, derived from Fisher's principle, especially Hamilton's (1967) concept of an unbeatable strategy. Maynard Smith was jointly awarded the 1999 Crafoord Prize for his development of the concept of evolutionarily stable strategies and the application of game theory to the evolution of behaviour.

这个概念源自于麦克阿瑟R. H. MacArthur和汉密尔顿W. D. Hamilton关于性别比例的研究，以及费雪原理Fisher's principle，另外尤其是汉密尔顿（1967）提出的“无敌战略Unbeatable Strategy“的概念。随后1999年，梅纳德·史密斯因其对“进化均衡策略”概念的发展，以及“行为进化博弈论“的应用研究做出了杰出贡献，与以上学者共同获得了著名的Crafoord奖。

Uses of ESS:

Uses of ESS: 进化均衡策略的应用

• The ESS was a major element used to analyze evolution in Richard Dawkins' bestselling 1976 book The Selfish Gene.

• 进化均衡策略是理查德·道金斯Richard Dawkins1976年最畅销的著作《自私的基因The Selfish Gene》中用来分析进化的主要元素。

• The ESS was first used in the social sciences by Robert Axelrod in his 1984 book The Evolution of Cooperation. Since then, it has been widely used in the social sciences, including anthropology, economics, philosophy, and political science.

• 由罗伯特·阿克塞尔罗德Robert Axelrod在1984年创作出版的《合作的进化The Evolution of Cooperation》一书中首次将进化均衡策略用于社会科学领域。从那时起，它就被广泛用于社会科学，包括人类学，经济学，哲学和政治学。

• In the social sciences, the primary interest is not in an ESS as the end of biological evolution, but as an end point in cultural evolution or individual learning.

• 在社会科学中，最主要的兴趣不是将进化均衡策略作为生物进化的终点，而是将其作为文化进化或个体学习的终点。

• In evolutionary psychology, ESS is used primarily as a model for human biological evolution.

• 在进化心理学中，进化均衡策略主要用作人类生物学进化的模型。

Motivation 策略的假设与动机

The Nash equilibrium is the traditional solution concept in game theory. It depends on the cognitive abilities of the players. It is assumed that players are aware of the structure of the game and consciously try to predict the moves of their opponents and to maximize their own payoffs. In addition, it is presumed that all the players know this (see common knowledge). These assumptions are then used to explain why players choose Nash equilibrium strategies.

The Nash equilibrium is the traditional solution concept in game theory. It depends on the cognitive abilities of the players. It is assumed that players are aware of the structure of the game and consciously try to predict the moves of their opponents and to maximize their own payoffs. In addition, it is presumed that all the players know this (see common knowledge). These assumptions are then used to explain why players choose Nash equilibrium strategies.

在博弈论中，纳什平衡相当于一种传统的解决方案概念，而这取决于玩家的认知能力。假定玩家知道游戏的结构，有意识地尝试预测对手的行动，并最大程度地提高自己的收益。另外，纳什平衡也假定所有玩家都知道这一点（请参阅常识性知识common knowledge）。后来这些假设又被用于解释为什么玩家会选择纳什平衡策略。

Evolutionarily stable strategies are motivated entirely differently. Here, it is presumed that the players' strategies are biologically encoded and heritable. Individuals have no control over their strategy and need not be aware of the game. They reproduce and are subject to the forces of natural selection, with the payoffs of the game representing reproductive success (biological fitness). It is imagined that alternative strategies of the game occasionally occur, via a process like mutation. To be an ESS, a strategy must be resistant to these alternatives.

Evolutionarily stable strategies are motivated entirely differently. Here, it is presumed that the players' strategies are biologically encoded and heritable. Individuals have no control over their strategy and need not be aware of the game. They reproduce and are subject to the forces of natural selection, with the payoffs of the game representing reproductive success (biological fitness). It is imagined that alternative strategies of the game occasionally occur, via a process like mutation. To be an ESS, a strategy must be resistant to these alternatives.

进化均衡策略的动机则完全不同。该策略被假定为具有生物编码性而且可遗传至下一代。玩家个人并不能控制自己的策略，也无需了解游戏规则。他们繁殖并服从自然选择，而游戏的收益则代表着繁殖成功（生物适应性）。同时可以想象，在繁殖过程中，游戏策略偶尔会通过类似基因突变而无计划地发生变异，产生其方案策略。之后他们会通过互相抵制直到出现最优势的策略，即进化均衡策略。

Given the radically different motivating assumptions, it may come as a surprise that ESSes and Nash equilibria often coincide. In fact, every ESS corresponds to a Nash equilibrium, but some Nash equilibria are not ESSes.

Given the radically different motivating assumptions, it may come as a surprise that ESSes and Nash equilibria often coincide. In fact, every ESS corresponds to a Nash equilibrium, but some Nash equilibria are not ESSes.

考虑到本质上全然不同的动机假设，进化均衡策略和纳什平衡偶尔的一致性可能令人港澳惊讶。实际上，每个进化均衡策略都有对应的纳什平衡，但是某些纳什平衡却不同于进化均衡策略。

Nash equilibrium

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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:

E(S,S) ≥ E(T,S)

进化均衡策略是纳什平衡的改进式（关于两者的对比，见下一章节）。在纳什平衡中，如果所有参与者都采用各自的策略方案，且都无法通过改用任何其他策略而从中获益。那么在该两人游戏中，我们将此看作一个策略对。令E(S,T)表示策略S对策略T的收益。当且仅当双方都成立且所有T≠S时，策略对（S，S）为该两人游戏中的纳什平衡： E(S,S) ≥ E(T,S)

In this definition, strategy T can be a neutral alternative to S (scoring equally well, but not better).

In this definition, strategy T can be a neutral alternative to S (scoring equally well, but not better).

在这个定义中，策略T可以成为S的中性替代（即最后得分相同，但并不更好）。

A Nash equilibrium is presumed to be stable even if T scores equally, on the assumption that there is no long-term incentive for players to adopt T instead of S. This fact represents the point of departure of the ESS.

A Nash equilibrium is presumed to be stable even if T scores equally, on the assumption that there is no long-term incentive for players to adopt T instead of S. This fact represents the point of departure of the ESS.

即使采用T后其得分相等，纳什平衡也被认为是稳定的，当然前提是假设不存在长期动机去鼓励玩家采用T而不是S。

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： 1. E(S,S) > E(T,S), or 2. E(S,S) = E(T,S) and E(S,T) > E(T,T)

The first condition is sometimes called a strict Nash equilibrium. The second is sometimes called "Maynard Smith's second condition". The second condition means that although strategy T is neutral with respect to the payoff against strategy S, the population of players who continue to play strategy S has an advantage when playing against T.

The first condition is sometimes called a strict Nash equilibrium. The second is sometimes called "Maynard Smith's second condition". The second condition means that although strategy T is neutral with respect to the payoff against strategy S, the population of players who continue to play strategy S has an advantage when playing against T.

第一个条件有时称为严格的纳什平衡。而第二个有时称为“梅纳德·史密斯的第二个条件”，它意味着，尽管策略T在对抗策略S时收益不变，但继续使用策略S的玩家在对抗策略T时收益具有明显优势。

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： 1. E(S,S) ≥ E(T,S)，并且 2. E(S,T) > E(T,T)，

In this formulation, the first condition specifies that the strategy is a Nash equilibrium, and the second specifies that Maynard Smith's second condition is met. Note that the two definitions are not precisely equivalent: for example, each pure strategy in the coordination game below is an ESS by the first definition but not the second.

In this formulation, the first condition specifies that the strategy is a Nash equilibrium, and the second specifies that Maynard Smith's second condition is met. Note that the two definitions are not precisely equivalent: for example, each pure strategy in the coordination game below is an ESS by the first definition but not the second.

在这两个公式中，第一个指定了该策略采取纳什平衡，而第二则是指定满足梅纳德·史密斯的第二个条件。请注意，这两个定义并不完全相等：例如，在接下来的协调游戏中的每个独立策略都是第一个定义的进化均衡策略，而非第二个。

In words, this definition looks like this: The payoff of the first player when both players play strategy S is higher than (or equal to) the payoff of the first player when he changes to another strategy T and the second player keeps his strategy S and the payoff of the first player when only his opponent changes his strategy to T is higher than his payoff in case that both of players change their strategies to T.

In words, this definition looks like this: The payoff of the first player when both players play strategy S is higher than (or equal to) the payoff of the first player when he changes to another strategy T and the second player keeps his strategy S and the payoff of the first player when only his opponent changes his strategy to T is higher than his payoff in case that both of players change their strategies to T.

换句话说，此定义还可以这么理解，当两个玩家都玩策略S时：1. 第一个玩家的收益要高于（或等于）当第一个玩家更改为策略T而第二个玩家保持策略S时的收益。2. 当第一个玩家的对手将策略更改为T时，第一个玩家自身的收益要大于他们两者都更改为策略T。

This formulation more clearly highlights the role of the Nash equilibrium condition in the ESS. It also allows for a natural definition of related concepts such as a weak ESS or an evolutionarily stable set.

This formulation more clearly highlights the role of the Nash equilibrium condition in the ESS. It also allows for a natural definition of related concepts such as a weak ESS or an evolutionarily stable set.

这种表述更清楚地强调了纳什平衡条件在进化均衡策略中的作用。同时还考虑到对相关概念进行自然定义，例如弱进化均衡策略Weak evolutionarily stable strategy或进化均衡集合Evolutionarily stable set。

Examples of differences between Nash equilibria and ESSes 纳什平衡与进化均衡策略之间差异的示例

囚徒困境prisoner's dilemma
	合作Cooperate	叛变Defect
合作Cooperate	3, 3	1, 4
叛变Defect	4, 1	2, 2

以邻为壑Harm thy neighbor
	A	B
A	2,2	1,2
B	2,1	2,2

In most simple games, the ESSes and Nash equilibria coincide perfectly. For instance, in the prisoner's dilemma there is only one Nash equilibrium, and its strategy (Defect) is also an ESS.

In most simple games, the ESSes and Nash equilibria coincide perfectly. For instance, in the prisoner's dilemma there is only one Nash equilibrium, and its strategy (Defect) is also an ESS.

在大多数简单的游戏中，进化均衡策略和纳什平衡完全重合。例如，在游戏《囚徒困境Prisoner's Dilemma》中，只有一个纳什平衡，其策略（叛变）也是一种进化均衡策略。

Some games may have Nash equilibria that are not ESSes. For example, in harm thy neighbor (whose payoff matrix is shown here) both (A, A) and (B, B) are Nash equilibria, since players cannot do better by switching away from either. However, only B is an ESS (and a strong Nash). A is not an ESS, so B can neutrally invade a population of A strategists and predominate, because B scores higher against B than A does against B. This dynamic is captured by Maynard Smith's second condition, since E(A, A) = E(B, A), but it is not the case that E(A,B) > E(B,B).

Some games may have Nash equilibria that are not ESSes. For example, in harm thy neighbor (whose payoff matrix is shown here) both (A, A) and (B, B) are Nash equilibria, since players cannot do better by switching away from either. However, only B is an ESS (and a strong Nash). A is not an ESS, so B can neutrally invade a population of A strategists and predominate, because B scores higher against B than A does against B. This dynamic is captured by Maynard Smith's second condition, since E(A, A) = E(B, A), but it is not the case that E(A,B) > E(B,B).

还有一些游戏可能具有非进化均衡策略的纳什平衡。例如，在游戏《以邻为壑Harm thy neighbor》中（此处显示为回报矩阵），（A，A）和（B，B）都是纳什平衡，因为玩家无法通过选择放弃任一个来做得更好。但是，只有B是进化均衡策略（也是强纳什）。A不是进化均衡策略，因此B可以中立地入侵A策略的群体并占据优势地位，因为B对B的得分要比A对B的得分高。由于E（A，A）= E（B，A），因此可以通过梅纳德·史密斯的第二个条件来捕获此动态，但是E（A，B）> E（B，B）并非如此。

伤害大家Harm everyone
	C	D
C	2,2	1,2
D	2,1	0,0

小鸡博弈The Game of Chicken
	转身离开Swerve	留下Stay
转身离开Swerve	0,0	-1,+1
留下Stay	+1,-1	-20,-20

Nash equilibria with equally scoring alternatives can be ESSes. For example, in the game Harm everyone, C is an ESS because it satisfies Maynard Smith's second condition. D strategists may temporarily invade a population of C strategists by scoring equally well against C, but they pay a price when they begin to play against each other; C scores better against D than does D. So here although E(C, C) = E(D, C), it is also the case that E(C,D) > E(D,D). As a result, C is an ESS.

Nash equilibria with equally scoring alternatives can be ESSes. For example, in the game Harm everyone, C is an ESS because it satisfies Maynard Smith's second condition. D strategists may temporarily invade a population of C strategists by scoring equally well against C, but they pay a price when they begin to play against each other; C scores better against D than does D. So here although E(C, C) = E(D, C), it is also the case that E(C,D) > E(D,D). As a result, C is an ESS.

纳什平衡以及同等评分的策略都可以是进化均衡策略。例如，在游戏《伤害大家Harm everyone》中，C是进化均衡策略，因为它满足了梅纳德·史密斯的第二条件。D策略可以暂时入侵C策略群体，因为D策略可以获得和C策略一样的评分。但是当他们开始互相对抗时，他们会付出一定的代价；C对D的得分比D对D的得分高。因此，尽管E（C，C）=E（D，C），但E（C，D）> E（D，D）。因此，最后C是最终进化均衡策略。

Even if a game has pure strategy Nash equilibria, it might be that none of those pure strategies are ESS. Consider the Game of chicken. There are two pure strategy Nash equilibria in this game (Swerve, Stay) and (Stay, Swerve). However, in the absence of an uncorrelated asymmetry, neither Swerve nor Stay are ESSes. There is a third Nash equilibrium, a mixed strategy which is an ESS for this game (see Hawk-dove game and Best response for explanation).

Even if a game has pure strategy Nash equilibria, it might be that none of those pure strategies are ESS. Consider the Game of chicken. There are two pure strategy Nash equilibria in this game (Swerve, Stay) and (Stay, Swerve). However, in the absence of an uncorrelated asymmetry, neither Swerve nor Stay are ESSes. There is a third Nash equilibrium, a mixed strategy which is an ESS for this game (see Hawk-dove game and Best response for explanation).

还有一些游戏即使具有纯粹的纳什均衡策略，但可能它们都不是进化均衡策略。比如游戏《小鸡博弈The Game of Chicken》,该游戏中有两种纯粹的纳什均衡策略（转身离开Swerve，留下Stay）和（留下Stay，转身离开Swerve）。但是，在无关联不对称Uncorrelated Asymmetry缺失的情况下，Swerve和Stay都不是进化均衡策略。此时存在第三种纳什平衡，它属于混合策略并且是该游戏的进化均衡策略（详情请参见《鹰鸽博弈Hawk-dove》游戏和《最佳响应Best Response》以获得解释）。

This last example points to an important difference between Nash equilibria and ESS. Nash equilibria are defined on strategy sets (a specification of a strategy for each player), while ESS are defined in terms of strategies themselves. The equilibria defined by ESS must always be symmetric, and thus have fewer equilibrium points.

This last example points to an important difference between Nash equilibria and ESS. Nash equilibria are defined on strategy sets (a specification of a strategy for each player), while ESS are defined in terms of strategies themselves. The equilibria defined by ESS must always be symmetric, and thus have fewer equilibrium points.

最后一个示例指出了纳什平衡与进化均衡策略之间的重要区别。纳什平衡是在策略集（每个参与者的策略规范）上定义的，而进化均衡策略是根据策略本身定义的。进化均衡策略定义的平衡必须始终是对称的，因此其平衡点更少。

Vs. evolutionarily stable state 与进化稳定状态的比较

In population biology, the two concepts of an evolutionarily stable strategy (ESS) and an evolutionarily stable state are closely linked but describe different situations.

In population biology, the two concepts of an evolutionarily stable strategy (ESS) and an evolutionarily stable state are closely linked but describe different situations.

在种群生物学中，进化均衡策略（ESS）和进化稳定状态Evolutionarily Stable State这两个概念密切相关，但却描述了不同的情况。

In an evolutionarily stable strategy, if all the members of a population adopt it, no mutant strategy can invade. Once virtually all members of the population use this strategy, there is no 'rational' alternative. ESS is part of classical game theory.

In an evolutionarily stable strategy, if all the members of a population adopt it, no mutant strategy can invade. Once virtually all members of the population use this strategy, there is no 'rational' alternative. ESS is part of classical game theory.

在进化均衡策略中，如果所有种群的成员都采用它，那么任何突变策略都无法入侵。无形中只要所有成员都使用了这种策略，就不再有“理性”的选择。进化均衡策略是经典博弈论的一部分。

In an evolutionarily stable state, a population's genetic composition is restored by selection after a disturbance, if the disturbance is not too large. An evolutionarily stable state is a dynamic property of a population that returns to using a strategy, or mix of strategies, if it is perturbed from that initial state. It is part of population genetics, dynamical system, or evolutionary game theory. This is now called convergent stability.

In an evolutionarily stable state, a population's genetic composition is restored by selection after a disturbance, if the disturbance is not too large. An evolutionarily stable state is a dynamic property of a population that returns to using a strategy, or mix of strategies, if it is perturbed from that initial state. It is part of population genetics, dynamical system, or evolutionary game theory. This is now called convergent stability.

在稳定的进化状态下，如果干扰不太大的话，即使受到冲击，种群的基因组成通过策略选择同样能够进行恢复。而进化稳定状态是种群的动态特性，即使受到初始状态的干扰，该状态会通过使用策略或混合策略组进行恢复。它是群体遗传学，动力学系统或进化博弈论的一部分。现在称为收敛稳定性。

B. Thomas (1984) applies the term ESS to an individual strategy which may be mixed, and evolutionarily stable population state to a population mixture of pure strategies which may be formally equivalent to the mixed ESS.

B. Thomas (1984) applies the term ESS to an individual strategy which may be mixed, and evolutionarily stable population state to a population mixture of pure strategies which may be formally equivalent to the mixed ESS.

托马斯B. Thomas（1984）将“进化均衡策略”这一术语应用于可混合的独立策略，并将“进化稳定种群状态”应用于采取纯策略的混合种群，该应用在形式上可能等同于混合的“进化均衡策略”。

Whether a population is evolutionarily stable does not relate to its genetic diversity: it can be genetically monomorphic or polymorphic.

Whether a population is evolutionarily stable does not relate to its genetic diversity: it can be genetically monomorphic or polymorphic.

种群是否在进化过程中处于稳定状态与它的基因多样性无关：它可以是遗传上的单态或多态的。

Stochastic ESS 随机的进化均衡策略

In the classic definition of an ESS, no mutant strategy can invade. In finite populations, any mutant could in principle invade, albeit at low probability, implying that no ESS can exist. In an infinite population, an ESS can instead be defined as a strategy which, should it become invaded by a new mutant strategy with probability p, would be able to counterinvade from a single starting individual with probability >p, as illustrated by the evolution of bet-hedging.

In the classic definition of an ESS, no mutant strategy can invade. In finite populations, any mutant could in principle invade, albeit at low probability, implying that no ESS can exist. In an infinite population, an ESS can instead be defined as a strategy which, should it become invaded by a new mutant strategy with probability p, would be able to counterinvade from a single starting individual with probability >p, as illustrated by the evolution of bet-hedging.

在进化均衡策略的经典定义中，没有任何突变策略可以入侵。然而在有限种群中，任何突变体原则上是可以入侵的，尽管可能性很小，这就意味着在这个种群中绝对没有进化均衡策略的存在。如果在无限种群中，存在一个概率为P的新突变策略入侵，此时，进化均衡策略就被认为是具有概率大于p的策略方案且开始反击最初入侵的新突变策略个体，就像对冲交易的进化过程描述那样。

Prisoner's dilemma

{{Payoff matrix | Name = Prisoner's Dilemma

1 d = 缺陷 | DL = 4,1 | DR = 2,2}

A common model of altruism and social cooperation is the Prisoner's dilemma. Here a group of players would collectively be better off if they could play Cooperate, but since Defect fares better each individual player has an incentive to play Defect. One solution to this problem is to introduce the possibility of retaliation by having individuals play the game repeatedly against the same player. In the so-called iterated Prisoner's dilemma, the same two individuals play the prisoner's dilemma over and over. While the Prisoner's dilemma has only two strategies (Cooperate and Defect), the iterated Prisoner's dilemma has a huge number of possible strategies. Since an individual can have different contingency plan for each history and the game may be repeated an indefinite number of times, there may in fact be an infinite number of such contingency plans.

A common model of altruism and social cooperation is the Prisoner's dilemma. Here a group of players would collectively be better off if they could play Cooperate, but since Defect fares better each individual player has an incentive to play Defect. One solution to this problem is to introduce the possibility of retaliation by having individuals play the game repeatedly against the same player. In the so-called iterated Prisoner's dilemma, the same two individuals play the prisoner's dilemma over and over. While the Prisoner's dilemma has only two strategies (Cooperate and Defect), the iterated Prisoner's dilemma has a huge number of possible strategies. Since an individual can have different contingency plan for each history and the game may be repeated an indefinite number of times, there may in fact be an infinite number of such contingency plans.

一种常见的利他主义和社会合作模式是囚徒困境。在这里，一组玩家如果能够玩合作游戏，那么他们的整体状况会更好，但是因为缺陷的收益更好，所以每个玩家都有一个玩缺陷游戏的动机。这个问题的一个解决方案是引入报复的可能性，让个人对同一个玩家重复进行游戏。在所谓的重复囚徒困境中，同样的两个人一遍又一遍地玩着囚徒困境。囚徒困境只有两种策略(合作策略和缺陷策略) ，重复囚徒困境有大量的可能策略。由于每个人可能对每个历史有不同的应急计划，而且游戏可能无限次地重复，因此事实上可能有无限次这样的应急计划。

Three simple contingency plans which have received substantial attention are Always Defect, Always Cooperate, and Tit for Tat. The first two strategies do the same thing regardless of the other player's actions, while the latter responds on the next round by doing what was done to it on the previous round—it responds to Cooperate with Cooperate and Defect with Defect.

Three simple contingency plans which have received substantial attention are Always Defect, Always Cooperate, and Tit for Tat. The first two strategies do the same thing regardless of the other player's actions, while the latter responds on the next round by doing what was done to it on the previous round—it responds to Cooperate with Cooperate and Defect with Defect.

三个受到广泛关注的简单应急计划是总是缺陷、总是合作和以牙还牙。前两种策略做同样的事情，而不管其他玩家的行动，而后者在下一轮做出回应，做上一轮做的事情ーー它回应与合作和缺陷合作。

If the entire population plays Tit-for-Tat and a mutant arises who plays Always Defect, Tit-for-Tat will outperform Always Defect. If the population of the mutant becomes too large — the percentage of the mutant will be kept small. Tit for Tat is therefore an ESS, with respect to only these two strategies. On the other hand, an island of Always Defect players will be stable against the invasion of a few Tit-for-Tat players, but not against a large number of them. If we introduce Always Cooperate, a population of Tit-for-Tat is no longer an ESS. Since a population of Tit-for-Tat players always cooperates, the strategy Always Cooperate behaves identically in this population. As a result, a mutant who plays Always Cooperate will not be eliminated. However, even though a population of Always Cooperate and Tit-for-Tat can coexist, if there is a small percentage of the population that is Always Defect, the selective pressure is against Always Cooperate, and in favour of Tit-for-Tat. This is due to the lower payoffs of cooperating than those of defecting in case the opponent defects.

If the entire population plays Tit-for-Tat and a mutant arises who plays Always Defect, Tit-for-Tat will outperform Always Defect. If the population of the mutant becomes too large — the percentage of the mutant will be kept small. Tit for Tat is therefore an ESS, with respect to only these two strategies. On the other hand, an island of Always Defect players will be stable against the invasion of a few Tit-for-Tat players, but not against a large number of them. If we introduce Always Cooperate, a population of Tit-for-Tat is no longer an ESS. Since a population of Tit-for-Tat players always cooperates, the strategy Always Cooperate behaves identically in this population. As a result, a mutant who plays Always Cooperate will not be eliminated. However, even though a population of Always Cooperate and Tit-for-Tat can coexist, if there is a small percentage of the population that is Always Defect, the selective pressure is against Always Cooperate, and in favour of Tit-for-Tat. This is due to the lower payoffs of cooperating than those of defecting in case the opponent defects.

如果整个种群都玩以牙还牙的游戏，而一个变种人出现了，他总是玩“缺陷”游戏，那么“以牙还牙”游戏就会胜过“总是缺陷”游戏。如果突变体的种群数量过大，则突变体的比例将保持在较小的水平。一报还一报因此是一个斯洛文尼亚就只有这两个战略。另一方面，一个永远有缺陷的玩家的岛屿可以稳定地对抗少数以牙还牙的玩家的入侵，但不能对抗大量的他们。如果我们引入总是合作，一个以牙还牙的群体就不再是 ESS 了。由于一群以牙还牙的玩家总是合作，策略总是合作在这群人中表现一致。因此，一个总是合作的变种人将不会被淘汰。然而，即使“永远合作”和“以牙还牙”的人群可以共存，如果有一小部分人“永远不合作” ，那么选择性的压力就是反对“永远合作” ，赞成“以牙还牙”。这是因为在对手缺陷的情况下，合作的回报低于背叛的回报。

This demonstrates the difficulties in applying the formal definition of an ESS to games with large strategy spaces, and has motivated some to consider alternatives.

This demonstrates the difficulties in applying the formal definition of an ESS to games with large strategy spaces, and has motivated some to consider alternatives.

这表明了在将 ESS 的形式化定义应用于具有大型战略空间的博弈中的困难，并促使一些人考虑其他选择。

Human behavior

The fields of sociobiology and evolutionary psychology attempt to explain animal and human behavior and social structures, largely in terms of evolutionarily stable strategies. Sociopathy (chronic antisocial or criminal behavior) may be a result of a combination of two such strategies.

The fields of sociobiology and evolutionary psychology attempt to explain animal and human behavior and social structures, largely in terms of evolutionarily stable strategies. Sociopathy (chronic antisocial or criminal behavior) may be a result of a combination of two such strategies.

社会生物学和进化心理学试图用进化稳定策略来解释动物和人类的行为和社会结构。反社会人格(慢性反社会或犯罪行为)可能是两种策略结合的结果。

Evolutionarily stable strategies were originally considered for biological evolution, but they can apply to other contexts. In fact, there are stable states for a large class of adaptive dynamics. As a result, they can be used to explain human behaviours that lack any genetic influences.

Evolutionarily stable strategies were originally considered for biological evolution, but they can apply to other contexts. In fact, there are stable states for a large class of adaptive dynamics. As a result, they can be used to explain human behaviours that lack any genetic influences.

进化稳定策略最初被认为是生物进化的策略，但它们可以应用于其他情况。事实上，对于一大类自适应动态系统，存在稳定状态。因此，它们可以用来解释没有任何遗传影响的人类行为。

See also

• Antipredator adaptation

• Behavioral ecology

• Evolutionary psychology

• Fitness landscape

• Hawk–dove game

• Koinophilia

• Sociobiology

• War of attrition (game)

Further reading

• Weibull, Jörgen (1997). Evolutionary game theory. MIT Press. ISBN 978-0-262-73121-8.  Classic reference textbook.

• Hines, W. G. S. (1987). "Evolutionary stable strategies: a review of basic theory". Theoretical Population Biology. 31 (2): 195–272. doi:10.1016/0040-5809(87)90029-3. PMID 3296292.

• Leyton-Brown, Kevin; Shoham, Yoav (2008). Essentials of Game Theory: A Concise, Multidisciplinary Introduction. San Rafael, CA: Morgan & Claypool Publishers. ISBN 978-1-59829-593-1. http://www.gtessentials.org. . An 88-page mathematical introduction; see Section 3.8. Free online at many universities.

• Parker, G. A. (1984) Evolutionary stable strategies. In Behavioural Ecology: an Evolutionary Approach (2nd ed) Krebs, J. R. & Davies N.B., eds. pp 30–61. Blackwell, Oxford.

• Shoham, Yoav; Leyton-Brown, Kevin (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. New York: Cambridge University Press. ISBN 978-0-521-89943-7. http://www.masfoundations.org. . A comprehensive reference from a computational perspective; see Section 7.7. Downloadable free online.

• Maynard Smith, John. (1982) Evolution and the Theory of Games.
  . Classic reference.

  
  

  External links

  • Evolutionarily Stable Strategies at Animal Behavior: An Online Textbook by Michael D. Breed.
  • Game Theory and Evolutionarily Stable Strategies, Kenneth N. Prestwich's site at College of the Holy Cross.
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  Category:Game theory equilibrium concepts

  范畴: 博弈论均衡概念

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  范畴: 进化博弈论

  
  

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