Memory-two zero-determinant strategies in repeated games

Abstract

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 $n\ge 2$ is also straightforward.

arXiv comment14 pages, 5 figures

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Cited by in corpus (9)

• Evolution of direct reciprocity in group-structured populations
• Necessary and Sufficient Condition for the Existence of Zero-Determinant Strategies in Repeated Games
• Unbeatable Tit-for-Tat as a Zero-Determinant Strategy
• Memory-two strategies forming symmetric mutual reinforcement learning equilibrium in repeated prisoners' dilemma game
• Controlling conditional expectations by zero-determinant strategies
• On the implementation of zero-determinant strategies in repeated games
• Unexploitable games and unbeatable strategies
• Autocratic strategies in Cournot oligopoly game
• On the existence of fair zero-determinant strategies in the periodic prisoner's dilemma game