Repeated games have provided an explanation how mutual cooperation can be achieved even if defection is more favorable in a one-shot game in prisoner's dilemma situation. Recently found zero-determinant strategies have substantially been investigated in evolutionary game theory. The original memory-one zero-determinant strategies unilaterally enforce linear relations between average payoffs of players. Here, we extend the concept of zero-determinant strategies to memory-two strategies in repeated games. Memory-two zero-determinant strategies unilaterally enforce linear relations between correlation functions of payoffs and payoffs at the previous round. Examples of memory-two zero-determinant strategy in the repeated prisoner's dilemma game are provided, some of which generalize the Tit-for-Tat strategy to memory-two case. Extension of zero-determinant strategies to memory-$n$ case with $n\geq 2$ is also straightforward.
翻译:重复游戏解释了如何实现相互合作,即使囚犯两难困境的一击游戏更有利于离队。最近发现的零决定性战略已经在进化游戏理论中进行了大量调查。最初的记忆-11零决定性战略单方面实施了球员平均报酬之间的线性关系。在这里,我们将零决定性战略的概念扩大到重复游戏中的记忆-二计战略。内存-二零决定性战略在上一回合中单方面强制实施报酬和报酬相关功能之间的线性关系。提供了囚犯两难游戏中的记忆-二零决定性战略的例子,其中一些战略将Tit-Tat战略概括为记忆-2案例。零决定性战略推广到以2美元计的记忆-一美元案例也是直截了当的。