  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.
