Group selection and social preferences ∗

Suppose that a large number of individuals are randomly matched into groups where each group plays a finite symmetric game. Individuals breed true according to their individual material payoffs, but the expected number of surviving offspring may depend on the material payoff vector to the whole group. We show that the mean-field equation for the induced population dynamic is equivalent to the replicator dynamic for a game with payoffs derived from those in the original game. We apply this selection dynamic to a number of examples, including prisoners’ dilemma games, coordination games, hawk-dove games, a prisoners’ dilemma with a punishment option, and common-pool games. For each of these, we provide conditions under which our selection dynamic leads to other outcomes than those obtained under the usual replicator dynamic. By way of a revealedpreference argument, we show how our selection dynamic can explain certain stable behaviors that are consistent with individuals having social preferences.