On the Emergence of Cooperation in the Repeated Prisoner's Dilemma

This article explores which parameters of the repeated Prisoner's Dilemma lead to cooperation. Using simulations, I demonstrate that the potential function of the stochastic evolutionary dynamics of the Grim Trigger strategy is useful to predict cooperation between Q-learners. The frontier separating the parameter spaces that induce either cooperation or defection can be determined based on the kinetic energy exerted by the respective basins of attraction. When the incentive compatibility constraint of the Grim Trigger strategy is slack, a sudden increase in the observed cooperation rates occurs when the ratio of the kinetic energies approaches a critical value, which itself is a function of the discount factor, multiplied by a correction factor to account for the effect of the algorithms' exploration probability. Using metadata from laboratory experiments, I provide evidence that the insights obtained from the simulations are also useful to explain the emergence of cooperation between humans. The observed cooperation rates show a positive gradient at the frontier characterized by an exploration probability of approximately five percent. In the context of human-to-human interaction, the exploration probability can be viewed as the belief about the opponent's probability to deviate from the equilibrium action.