  Two-player games have had a long and fruitful history of applications
stretching across the social, biological, and physical sciences. Most
applications of two-player games assume synchronous decisions or moves even
when the games are iterated. But different strategies may emerge as preferred
when the decisions or moves are sequential, or the games are iterated.
Zero-determinant strategies developed by Press and Dyson are a new class of
strategies that have been developed for synchronous two-player games, most
notably the iterated prisoner's dilemma. Here we apply the Press-Dyson analysis
to sequential or asynchronous two-player games. We focus on the asynchronous
prisoner's dilemma. As a first application of the Press-Dyson analysis of the
asynchronous prisoner's dilemma, tit-for-tat is shown to be an efficient
defense against extortionate zero-determinant strategies. Nice strategies like
tit-for-tat are also shown to lead to Pareto optimal payoffs for both players
in repeated prisoner's dilemma.
