  Repeated games have provided an explanation how mutual cooperation can be
achieved even if defection is more favorable in a one-shot game in prisoner's
dilemma situation. Recently found zero-determinant strategies have
substantially been investigated in evolutionary game theory. The original
memory-one zero-determinant strategies unilaterally enforce linear relations
between average payoffs of players. Here, we extend the concept of
zero-determinant strategies to memory-two strategies in repeated games.
Memory-two zero-determinant strategies unilaterally enforce linear relations
between correlation functions of payoffs and payoffs at the previous round.
Examples of memory-two zero-determinant strategy in the repeated prisoner's
dilemma game are provided, some of which generalize the Tit-for-Tat strategy to
memory-two case. Extension of zero-determinant strategies to memory-$n$ case
with $n\geq 2$ is also straightforward.
