Individual and Group Selection in Symmetric 2-Player Games

A population of individuals is divided into groups. Individuals are recurrently randomly matched with individuals from their group to play a generic symmetric 2-player game. Deterministic inter- and intra-group dynamics are derived from a model of individual imitation within groups and individual migration between groups. Conditions are identified under which subsets (components) of the set of stationary states are (interior) asymptotically stable. The results are then applied to generic coordination games and the prisoners' dilemma. The unique asymptotically stable set of stationary states in coordination games is such that every individual in non-extinct groups plays the Pareto-optimal equilibrium. In the multi-group prisoners' dilemma there is no asymptotically stable subset of the set of stationary states.