Equilibrium selection and the dynamic evolution of preferences

A population of fully rational agents play a symmetric 2-player game in biological fitnesses, but each agent’s play is determined by his payoffs, which are free to evolve according to “survival of the fittest” pressures. An equilibrium-selection mechanism is assumed to exist, and deliver a unique outcome for any given profile of payoffs; this allows the evolution of payoffs to be modeled as a well-defined replicator dynamics. The existing static stability results that “efficient strict Nash implies stability” and “stability implies efficiency” are translated to this dynamic context. Moreover, a strong form of stability is established for the efficient outcome of games with common interests, whilst weaker stability results are provided for nonstrict efficient equilibria (including mixed-strategy equilibria) of doubly symmetric games. The results are illustrated using the equilibrium-selection mechanism provided by global games. Journal of Economic Literature Classification Number: C72.