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

TL;DR

This paper demonstrates that the Tit-for-Tat strategy in repeated symmetric games is a zero-determinant strategy that unilaterally equalizes payoffs, specifically when the stage game is a potential game, revealing a link between unbeatable strategies and zero-determinant strategies.

Contribution

It establishes that Tit-for-Tat is a zero-determinant strategy under potential game conditions, connecting unbeatable strategies with zero-determinant properties.

Findings

Tit-for-Tat is a zero-determinant strategy in potential games.

Unbeatable property of Tit-for-Tat is equivalent to zero-determinant strategy.

The relation between zero-determinant strategies and unbeatable strategies is clarified.

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.