Migration and the evolution of conventions

Résumé

This paper analyzes an evolutionary model where agents are locally matched to playa coordination game and can adjust both their strategy and location. Their decisions are subject to friction, so that an agent who migrates to a different location may be unable to adjust her strategy optimally to the new environment. A condition on off-equilibrium payoffs introduced by Aumann (1993) plays a major role in our characterization (for general coordination games) of the long-run outcomes. For the particular 2 x 2 case, this condition (which is unrelated to risk dominance) implies that the possibility of medium term simultaneous co-existence of conventions at different locations depends on whether the game is of "pure" coordination (where co-existence is always possible) or of the stag'-hunt type (where it is not). When we introduce noise (Le. mutations) into the model, this distinction continuous to play a crucial role in the selection of the long'-run equilibria: for large friction, both equilibria are stochastically stable in the former case, whereas only the efficient one is so in the latter.