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 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:

斯洛文尼亚应用服务系统是纳什均衡点应用服务系统的改进或修改形式。(请参阅下一节中对比两者的例子。)在纳什均衡点游戏中，如果所有玩家都采用各自的角色，没有玩家可以通过切换到任何替代策略而获益。在两人博弈中，这是一对策略。设 e (s，t)表示策略 s 对策略 t 的收益。策略对(s，s)是双人博弈中的纳什均衡点对，当且仅当这对双方都成立且 t ≠ s 时:

E(S,S) ≥ E(T,S)

E(S,S) ≥ E(T,S)

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 可以是 s 的一个中性替代品(得分同样好，但不是更好)。

<！例如，在《伤害你的邻居》中，(a，a)是一个纳什均衡点，因为一个人不能通过转换到 b 来做得更好。* * 将把这一部分移到“比较”部分，尽量避免在同一段落中将 a & b 和科技策略混为一谈 -- >

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 t 得分相同，一个纳什均衡点也被认为是稳定的，前提是玩家没有长期的动机去使用 t 而不是 s。这一事实代表了斯洛文尼亚就业服务局的出发点。

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

Maynard Smith 和 Price 为策略 s 指定了两个成为 ESS 的条件。对于所有 t ≠ s，也是如此

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

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

E (s，s) > e (t，s) ，或

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

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

E (s，s) = e (t，s)和 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.

第一种情况有时被称为严格的纳什均衡点。第二种情况有时被称为“梅纳德 · 史密斯的第二种情况”。第二个条件意味着尽管策略 t 相对于策略 s 的收益是中性的，但是继续使用策略 s 的玩家在对抗策略 t 时有优势。

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

由于托马斯的缘故，还有另一种更强有力的 ESS 定义。这就不同程度地强调了纳什均衡点概念在斯洛文尼亚就业服务系统中的作用。根据上面第一个定义中给出的术语，这个定义要求对于所有 t ≠ s

1. E(S,S) ≥ E(T,S), and

E(S,S) ≥ E(T,S), and

E(S,S) ≥ E(T,S), and

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

E(S,T) > E(T,T)

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.

在这个公式中，第一个条件指定策略是纳什均衡点，第二个条件指定 Maynard Smith 的第二个条件是满足的。请注意，这两个定义并不完全等价: 例如，下面协调博弈中的每个纯策略按照第一个定义都是 ESS，但不是第二个定义。

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，这个定义是这样的: 当第一个参与人同时使用策略 s 时，第一个参与人改用另一个策略 t 时，第一个参与人的收益大于(或等于)第一个参与人改用策略 t 时的收益，第二个参与人保留策略 s 时的收益，第一个参与人改用策略 t 时的收益大于第一个参与人改用策略 t 时的收益。

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.

这个公式更清楚地强调了纳什均衡点条件在斯洛文尼亚就业服务系统中的作用。它还允许相关概念的自然定义，如弱 ESS 或进化稳定集。

Examples of differences between Nash equilibria and ESSes

{ | align = block

模板:Payoff matrix 1 d = 缺陷 | DL = 4,1 | DR = 2,2}

模板:Payoff matrix 1 d = b | DL = 2,1 | DR = 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.

在最简单的博弈中，ESSes 和纳什均衡完全吻合。例如，在囚徒困境中只有一个纳什均衡点，它的策略(缺陷)也是一个 ESS。

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).

有些博弈可能有非雌性的纳什均衡。例如，在伤害你的邻居(其收益矩阵在这里显示)两者(a，a)和(b，b)都是纳什均衡，因为玩家不能通过从其中任何一个切换来做得更好。然而，只有 b 是 ESS (和强 Nash)。不是 ESS，因此 b 可以中立地入侵 a 战略家的人群并占主导地位，因为 b 对 b 的得分高于 a 对 b 的得分。这个动态被 Maynard Smith 的第二个条件所捕获，因为 e (a，a) = e (b，a) ，但是它不是 e (a，b) > e (b，b)的情况。

{ | align = block style = “ clear: right”

模板:Payoff matrix 1 d = d | DL = 2,1 | DR = 0,0}

模板:Payoff matrix 1D = 停留 | DL = + 1,-1 | DR =-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.

具有相同得分的替代方案的纳什均衡可以是。例如，在游戏 Harm everyone 中，c 是一个 ESS，因为它满足 Maynard Smith 的第二个条件。D 战略家可能会暂时侵入 c 战略家群体，因为他们对 c 的得分同样高，但是当他们开始互相竞争时，他们付出了代价; c 对 d 的得分比 d 高。这里虽然 e (c，c) = e (d，c) ，但是 e (c，d) > e (d，d)的情况也是如此。因此，c 是一个 ESS。

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).

即使一个博弈有纯策略纳什均衡，也可能没有纯策略是 ESS。想想胆小鬼的游戏。在这个博弈中有两个纯策略纳什均衡(Swerve，Stay)和(Stay，Swerve)。然而，在没有不相关的不对称性的情况下，Swerve 和 Stay 都不是 ESSes。还有第三个纳什均衡点，一个混合策略，这是一个 ESS 的游戏(见鹰鸽游戏和最佳对策解释)。

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.

最后这个例子指出了纳什均衡和 ESS 之间的一个重要区别。纳什均衡是在策略集上定义的(每个参与者的策略规格) ，而 ESS 则是根据策略本身定义的。由 ESS 定义的平衡点必须总是对称的，因此平衡点较少。

Vs. evolutionarily stable state

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，evolutional stable strategy 和进化稳定状态这两个概念紧密相连，但描述的情况却不同。

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 evolutional stable strategy 中，如果一个种群的所有成员都采用它，那么任何变异策略都不能入侵。一旦几乎所有的人都使用这种策略，就没有理性的选择了。ESS 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.

在进化稳定状态下，如果干扰不太大，通过干扰后的选择恢复种群的遗传组成。进化稳定状态是种群的一个动态特性，当种群从初始状态受到扰动时，它会返回到使用策略或混合策略的状态。这是群体遗传学、动力系统或者进化博弈论的一部分。现在称之为收敛稳定性。

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(1984)将 ESS 一词应用于可能混合的个体策略，而将进化稳定的种群状态应用于纯策略的种群混合，这种混合策略在形式上等价于混合的 ESS。

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.

一个种群是否进化稳定与其遗传多样性无关: 它可以是遗传单态或多态的。

Stochastic ESS

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 ESS 的经典定义中，任何突变策略都不能入侵。在有限的群体中，任何突变体原则上都可以入侵，尽管概率很低，这意味着没有 ESS 可以存在。在一个无限种群中，ESS 可以被定义为一种策略，当它被一个新的概率为 p 的突变策略入侵时，它能够以概率大于 p 的方式从一个单独的起始个体中反击入侵，这可以用下注对冲的进化来说明。

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

  Category:Evolutionary game theory

  范畴: 进化博弈论

  
  

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