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

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