更改

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.

'''<font color="#ff8000"> 进化均衡策略Evolutionarily Stable Strategy（ESS）</font>'''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。进化均衡策略是'''<font color="#ff8000"> 纳什均衡Nash equilibrium</font>'''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。该理论并非通过有目的性地处理外部总体环境可能发生的变化，来引入新的种群进化选择力。

'''<font color="#ff8000"> 进化均衡策略Evolutionarily Stable Strategy（ESS）</font>'''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。进化均衡策略是'''<font color="#ff8000"> 纳什均衡Nash equilibrium</font>'''的细化，相当于是稳定进化的纳什均衡：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。该理论并非通过有目的性地处理外部总体环境可能发生的变化，来引入新的种群进化选择力。

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.

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.

E(S,S) ≥ E(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：

进化均衡策略是纳什均衡的改进式（关于两者的对比，见下一章节）。在纳什均衡中，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均衡：

E(S,S) ≥ E(T,S)

E(S,S) ≥ E(T,S)

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.

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.

2. E(S,T) > E(T,T)，

2. E(S,T) > E(T,T)，

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。它不同于纳什均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

1. E(S,S) ≥ E(T,S)，并且

2. E(S,T) > E(T,T)，

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.

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。

这种表述更清楚地强调了纳什均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 ===

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

{| class="wikitable"

{| class="wikitable"

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。

在大多数简单的游戏中，进化均衡策略和纳什均衡完全重合。例如，在游戏《囚徒困境Prisoner's Dilemma》中，只有一个纳什均衡，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。

还有一些游戏可能具有非进化均衡策略的纳什均衡。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）都是纳什均衡，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。

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。

纳什均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）。

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均衡，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.