Simple guilt and cooperation

We introduce simple guilt into a generic prisoner’s dilemma (PD) game and solve for the equilibria of the resulting psychological game. It is shown that for all guilt parameters, it is a pure strategy equilibrium that both players defect. But if the guilt parameter surpasses a threshold, a mixed strategy equilibrium and a pure strategy equilibrium in which both players cooperate emerge. We implement three payoff constellations of the PD game in a laboratory experiment and find in line with our equilibrium analysis that first- and second-order beliefs are highly correlated and that the probability of cooperation depends positively on these beliefs. Maximum likelihood estimations of a model of noisy introspection reveal that experimental data is best fitted with positive guilt levels and that omission of guilt results in a substantial increase in the noise parameters.