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

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.