Repeated games have provided an explanation of how mutual cooperation can be achieved even if defection is more favourable in a one-shot game in the Prisoner’s Dilemma situation. Recently found zero-determinant (ZD) strategies have substantially been investigated in evolutionary game theory. The original memory-one ZD strategies unilaterally enforce linear relationships between average pay-offs of players. Here, we extend the concept of ZD strategies to memory-two strategies in repeated games. Memory-two ZD strategies unilaterally enforce linear relationships between correlation functions of pay-offs and pay-offs of the previous round. Examples of memory-two ZD strategy in the repeated Prisoner’s Dilemma game are provided, some of which generalize the tit-for-tat strategy to a memory-two case. Extension of ZD strategies to memory-n case with n ≥ ̃2 is also straightforward.

重复的游戏解释了即使在囚徒困境情况下单发游戏中叛逃更为有利的情况下如何实现相互合作。最近发现的零决定因素（ZD）策略已在进化博弈论中得到了实质性的研究。原始的记忆一ZD策略会单方面强制玩家平均收益之间的线性关系。在这里，我们将ZD策略的概念扩展到重复游戏中的记忆二策略。记忆两个ZD策略会单方面强制执行收益与上一轮收益的相关函数之间的线性关系。提供了在重复囚徒困境游戏中采用记忆二的ZD策略的示例，其中一些将“针锋相对”策略推广到了记忆二的情况。将ZD策略扩展到内存-Ñ情况下与Ñ ≥2也是直截了当的。