Evolutionary dynamics with large aggregate shocks

This paper examines a class of evolutionary models in which large shocks cause frequent movement between short-term "stable" equilibria. Mutations are rare in our model, but their effects are magnified by a "spread process" which causes a finite proportion of the population to initially adopt the entering strategy before the short-term selection dynamics takes effect. We examine the long run invariant distribution for a variety of games, under several different spread processes: most interestingly, we find that cooperative strategies prevail in the long run in the Finitely Repeated Prisoner's Dilemma game, contrary to the backward induction solution. We also study equilibrium selection in 2x2 and NxN coordination games, establishing conditions under which the risk-dominant equilibrium is selected, and demonstrate rapid convergence to the long run invariant distribution.