Press-Dyson Analysis of Asynchronous, Sequential Prisoner's Dilemma

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.