Categorization and cooperation across games

We study a model where agents face a continuum of two-player games and categorize them into a finite number of situations to make sense of their complex environment. Each agent can cooperate or defect, conditional on the perceived category. Agents may not share the same categorization. The games are fully ordered by one parameter, interpreted as the temptation to break joint cooperation by defecting. We prove that in equilibrium agents must share the same categorization. Most equilibria achieve less cooperation than it would be possible if agents could fully discriminate games. All the equilibria are evolutionarily stable, but the only stochastically stable profile leads to defection everywhere, destroying all opportunities for cooperation. We then study agents’ social learning when they imitate successful players over similar games, but lack any information about the categorizations of other players. We show how imitation leads to a shared categorization that achieves higher cooperation than under full discrimination.