Charles Efferson (LEG Seminar 2025/11/18)

Repeated interactions enjoy favorable status as an explanation for the evolution of human cooperation. So favorable, in fact, that one influential hypothesis offers repeated interactions as a key mechanism behind human cooperation in anonymous one-shot settings. Some studies, however, suggest that repeated interactions in isolation, given a suitably flexible strategy space, do not reliably support cooperation. Using basic analytical results and a large number of simulations, I consider this question with a social dilemma involving a continuous action space. Continuous action spaces are important for at least two reasons. First, they arguably capture the social dilemmas people play in their daily lives better than games in which players can only choose to cooperate fully or defect fully. Second, they allow us to study the effects of extending the strategy space without positing players who can remember long histories of past play. Under repeated play of such a game, I examine eight strategy spaces and seven approaches to implementation errors in all combinations. Results show an overall pattern of limited cooperation. In particular, given some combination of strategy space and implementation error that does support the evolution of cooperative strategies, some suitable extension of the strategy space typically destabilizes cooperation. Although these results are not general, they are consistent with the notion that repeated interactions, as a stand-alone mechanism, only tend to support the evolution of cooperation given arbitrary restrictions on the strategy space.