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

翻译：零确定性战略是重复游戏中的一类记忆-一战略,单方面强制实施付款之间的线性关系,长期以来一直不清楚是否存在零确定性战略的阶段,我们为零确定性战略的存在提供了必要和充分的条件。这一条件可以被解释为存在两种不同的行动,它们单方面调整付款线性组合的总价值。还提供存在零确定性战略的阶段性游戏类别与其他阶段性游戏类别之间的关系。