Unbeatable Tit-for-Tat as a Zero-Determinant Strategy

Abstract

Tit-for-Tat strategy is a strategy in repeated two-player symmetric games which imitates the previous action of the opponent. We show that the Tit-for-Tat strategy is a zero-determinant strategy, which unilaterally equalizes the expected payoffs of two players, if and only if the stage game is a potential game. Because it has been known that this condition is equivalent to the condition that the Tit-for-Tat strategy is unbeatable, our results suggest some relation between unbeatable property and the concept of zero-determinant strategy.

arXiv comment21 pages

References in corpus (10)

• Autocratic strategies for iterated games with arbitrary action spaces
• Extortion under Uncertainty: Zero-Determinant Strategies in Noisy Games
• Unbeatable Imitation
• Pure Saddle Points and Symmetric Relative Payoff Games
• Autocratic strategies for alternating games
• Combination with anti-tit-for-tat remedies problems of tit-for-tat
• Five rules for friendly rivalry in direct reciprocity
• Memory-two zero-determinant strategies in repeated games
• Linear algebraic structure of zero-determinant strategies in repeated games
• Tit-for-Tat Strategy as a Deformed Zero-Determinant Strategy in Repeated Games

Cited by in corpus (7)

• Necessary and Sufficient Condition for the Existence of Zero-Determinant Strategies in Repeated Games
• 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
• Properties of zero-determinant strategies in multichannel games
• On the existence of fair zero-determinant strategies in the periodic prisoner's dilemma game