Price of fairness for zero-determinant strategies in Iterated Prisoner’s Dilemma

Abstract

It’s known that one player adopts the zero-determinant strategy can enforce a linear relation between players in two-player Iterated Prisoner’s Dilemma (IPD) games. In this case, the player takes an unfair share which makes her opponent no incentive for cooperation, even leads to a lower system welfare. In this paper, we study the fair solution of zero-determinant strategies and adopt price of fairness to measure the quality of a fair solution. We first consider the situation that one player adopts zero-determinant strategies in IPD, in which some properties holding for zero-determinant strategies are provided. Furthermore, we explore the bounds about price of fairness under three different definitions of fairness, namely maximin, Kalai-Smorodinski and proportional fairness.