Studying Negative Rationality in Quantal Response Equilibrium

In this paper, we present an investigation of the negative parameter of rationality in a symmetrical quantal response equilibrium (QRE) in the Prisoner's Dilemma game (PD) constructed in Markov strategies (tolerance to defection and mutual cooperation). We characterize the behavior of a new branch of equilibrium through the considered strategies. Also, we compare the theoretically found equilibrium in the area of negative rationality with the experimental data: we observe that this part of equilibrium corresponds with a high level of cooperation close to 100%. Thus, we propose that the negative rationality in QRE could be considered as a new theoretical approximation to unconditional cooperation.