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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。
 
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。
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== Prisoner's dilemma ==
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== Prisoner's dilemma 囚徒困境 ==
    
{{Payoff matrix | Name = Prisoner's Dilemma
 
{{Payoff matrix | Name = Prisoner's Dilemma
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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.
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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。
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利他主义和社会合作的普遍模式就是囚徒的困境。在这里,如果一群玩家选择“合作”,那么他们这个集体就会生活的更好,但是由于“背叛”带来的利益更大,因此每个玩家都有动机去选择“背叛”。解决该问题的其中一个方案是通过让个体反复与同一玩家来对战,以此引入报复机制的可能性。在所谓的囚徒困境迭代过程中,相同的两个人一遍又一遍地扮演着她们的角色。尽管囚犯的困境只有两种策略(合作和背叛),但迭代的囚徒困境游戏却具有大量可能的策略。由于个体对于每个历史可以具有不同的应急计划,并且游戏可以无限次重复,因此实际上可能有无限个此类应急计划。
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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.
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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。
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其备受关注的三个简单的应急计划是:“始终背叛”,“始终合作”和“针锋相对”。前两种策略会始终执行相同的操作,而不受另一方行为的影响,而后一种策略则是通过上一轮中执行的操作来对下一轮中的对象做出响应-其响应为“合作对合作”和“背叛对背叛”。
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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.
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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。
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如果整个种群都选择“针锋相对”,并且出现了一个变异者选择了“始终背叛”,那么“针锋相对”将战胜“始终背叛”。如果该变异者的种群太大,则它所占的百分比将保持很小。因此,就这两种策略而言,“针锋相对”就是一种进化均衡策略。另一方面,“始终背叛”的玩家群体可以稳定地抵御少数“针锋相对”玩家的入侵,但不能抵御大量的入侵。
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如果我们引入“始终合作”,那么“针锋相对”就不再是进化均衡策略了。由于大量的“针锋相对”玩家转向选择保持合作,因此“始终合作”策略在这一群体中的表现相同。最终,“始终合作”的变异者将不会被淘汰。当然,即使“始终合作”和“针锋相对”的人群可以共存,但是如果“始终背叛”的玩家总量只占一小部分时,那么策略选择压力会对“始终合作”不利,而倾向于支持“针锋相对”。这是由于合作带来的利益要比背叛来的低。
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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.
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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。
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这证明了要想将进化均衡策略的正式定义应用于具有较大策略空间的游戏中,是非常困难的。因此促使了一些人去考虑替代方案。
    
== Human behavior ==
 
== Human behavior ==
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