Delayed Evolutionary Game Dynamics applied to Medium Access Control

A major contribution of biology to competitive decision making is the development of the discipline of evolutionary games. Its ESS (evolutionary stable strategy) equilibrium concept, well adapted to large populations of players, describes robustness against deviations of a whole fraction of the population (in contrast to Nash equilibrium that requires robustness against a single user´s deviation). The second appealing element of evolutionary games, the replicator dynamics, describes the evolution of strategies in time. Under suitable conditions, this (and some other) dynamics, converge to an ESS. In this paper we study the effect of slow time scale delays on the convergence of various dynamics. We apply this to an evolutionary game describing competition between mobile terminals over the access to a common channel.