Reciprocal altruism is considered to be a strong mechanism that can promote cooperation, if individuals are likely to interact. Experimental evidence shows that most of the people have reciprocal tendencies when they interact in social dilemma experiments, although the members of the population as a whole seem to be heterogeneous in terms of their conditional strategies. In addition to that, those who employ conditionally cooperative strategies also seem to have a certain degree of selfish bias; they tend to give less than what others give do. Cooperation by the individuals who employ such preferences is bound to collapse as the level of cooperation tends to decrease over time.
In this study, we investigate conditional types and their evolution in an iterated Prisoner's Dilemma , comparing different continuation probabilities, by using a computational model. In our setting, agents are characterized by their responses to each level of cooperation in a linearly extended Prisoner's Dilemma. By using repeated simulations, we estimate the likelihood of cooperation and the conditional strategies that are likely to succeed.
Our results show that, when the continuation probability is sufficiently large, full cooperation is achieved. In this case, the most successful strategies are the ones who employ an all-or-none type of conditional cooperation, followed by perfect conditional cooperators. In the intermediate levels of continuation probability, however, hump-shaped contributor types are the ones that are most likely to exist, followed by imperfect conditional cooperators. Those agents cooperate in a medium level of cooperation within themselves and each other.
Our results provide an explanation for the commonly observed hump-shaped strategy and imperfect conditional cooperators in experiments. Furthermore, a potential implication of our results is that the heterogeneity of conditional strategies might stem from the diverse interaction frequencies among real-world interactions.