Probability Biases in Repeated Prisoner’s Dilemma Game
This paper 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 had a fixed and known continuation probability, which can be interpreted as time discounting under the standard discounted expected utility model. Under the assumption of constant discounting, 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 21% of the subjects have risk preferences best described by prospect theory with small probabilities overweighed (i.e., optimism) and large ones underweighted (i.e., pessimism). Some players are always pessimistic (26%), whereas many (53%) are expected utility (EU) players. The main finding is that the cooperation level is correlated with the type of biases. Specifically, for all continuation probabilities, PT-type subjects cooperate more than EU subjects, and pessimistic subjects cooperate less than EU subjects. We explain this behaviour in repeated games by adopting Halevy’s impatience index.