Sleepers, Thresholds, and Gateways : Drift and Stability in the Ultimatum Game and the Prisoners’ Dilemma

The dynamics generated by individual learning mechanisms in evolutionary games rely upon the relationship between imitation and experimentation. We consider the dynamics created by individuals who learn through a process of selective imitation, for a general class of sequential, symmetric, binary-choice (SSBC) games. In particular we simulate these dynamics for two well known games: the ultimatum game and the prisoner's dilemma. Our paper shows how the evolutionary stability characteristics of SSBC games combines with inevitable drift in selective imitation dynamics to create a potential for periods of time spent away from what might otherwise be considered strong Nash equilibria. The conditions for evolutionary dynamics that move a system away from equilibrium behaviour depend upon the existence of sleeper strategies, invasion thresholds and exit gateways