Quantal response equilibrium for the Prisoner’s Dilemma game in Markov strategies

Abstract

Within the studies of human cooperation, there are gaps that require further investigation. One possible area for growth is developing theoretical concepts which describe high levels of cooperation. In this paper, we present a symmetrical quantal response equilibrium (QRE) in Prisoner’s Dilemma game (PD) constructed in Markov strategies (tolerance to defection and mutual cooperation). To prove the adequacy of the resulting equilibrium, we compare it with the previously found Nash equilibrium in PD in Markov strategies: the QRE converges with the Nash equilibrium that corresponds with the theory. Next, we investigate the properties of QRE in PD in Markov strategies by testing it against experimental data. For low levels of rationality, the found equilibrium manages to describe high cooperation. We derive the levels of rationality under which the intersection between Nash and QRE occurs. Lastly, our experimental data suggest that QRE serves as a dividing line between behavior with low and high cooperation.