  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.

Physics and Society