Play Locally, Learn Globally: The Structural Basis of Cooperation

In group-structured populations, altruistic cooperation among unrelated group members may be sustainable even when the evolution of behavioral traits is governed by a payoff-based replicator dynamic. This paper explores the importance in this dynamic of two aspects of group structure: interaction in a public goods game and the cultural transmission of behavioral traits. Agents are paired with others to play the game and (independently of this) to learn from a cultural model. Where pairing is global, one's game partners and cultural model are drawn from the entire population. Or pairing may be local, in which case one's game partners will be the same from period to period, and one's cultural models will be drawn from one's game partners. To clarify the underlying dynamic, I derive an extension of the price equation for the decomposition of changes in the population frequency of a binary trait and analyze the effect of different structures of social interaction on within- and between-group variances and on the evolution of cooperation. The simulations reported below use a genetic algorithm to explore a large strategy space for this problem, and to study the dynamics of this population. I show that of the four population structures given by global and local learning and global and local game interaction, local interaction with global learning provides the most favorable environment for the evolution of cooperation. This occurs because this combination of learning and interaction structures supports a high level of between-group variance in the frequency of cooperative types, so that most cooperators benefit from being in groups composed mostly of cooperators. However, neither global learning nor local interaction is sufficient by itself to support high levels of cooperation. Learning globally and playing locally are thus highly complementary: global learning in the presence of global interactions or local interaction in the presence of local learning, makes little contribution to the evolutionary success of cooperative traits.