Probability Biases in Repeated Prisoner’s Dilemma Game

This study provides evidence that biases attributed to the perception of probabilities affect cooperation levels in repeated games. In an experiment, subjects completed a prisoner’s dilemma game that continued to the next round with a fixed probability. Under the standard assumption of (constant) discounted expected utility, such a probability can be interpreted as time discounting. The presence of probability biases leads to deviations from constant discounting, as shown in Halevy (2008, AER), which then affects the evaluation of the outcomes in the game and, the hypothesis is that this affects the cooperate-defect decision of subjects. Using an incentive-compatible mechanism based on scoring rules, we quantify the direction and magnitude of subjects’ probability bias. We find that 53% of subjects are expected utility (EU) subjects; 21% of subjects reveal biases that accord with prospect theory: small probabilities are overweighted and medium to large ones are underweighted (inverse-S); 26% of subjects underestimate small probabilities and overestimate large probabilities (S-shape). The main finding is that the cooperation level is correlated with the type of biases. Specifically, for all continuation probabilities, inverse-S subjects cooperate more than EU subjects, and S-shape subjects cooperate less than EU subjects. We explain this behaviour in repeated games by adopting Halevy’s impatience index.