Necessary and Sufficient Condition for the Existence of Zero-Determinant Strategies in Repeated Games

Zero-determinant strategies are a class of memory-one strategies in repeated\ngames which unilaterally enforce linear relationships between payoffs. It has\nlong been unclear for what stage games zero-determinant strategies exist. We\nprovide a necessary and sufficient condition for the existence of\nzero-determinant strategies. This condition can be interpreted as the existence\nof two different actions which unilaterally adjust the total value of a linear\ncombination of payoffs. A relation between the class of stage games where\nzero-determinant strategies exist and other class of stage games is also\nprovided.\n