On delayed discrete evolutionary dynamics

We examine the asymptotic stability of equilibria where individuals react to delayed information and the delays are heterogeneously distributed. For symmetric games with binary actions, we derive conditions under which the stability/instability of equilibria does not depend on the delay distribution. As a corollary, we show that a unique mixed evolutionarily stable state in games in well-mixed populations is asymptotically stable under a class of delayed replicator dynamics, for any lag distribution.

► We examine the evolutionary stability of equilibria where individuals react to delayed information.
► We allow delays to be heterogeneously distributed within a population.
► We derive conditions under which the stability/instability of equilibria does not depend on the detail of delay distribution.
► As a corollary, a unique mixed equilibrium is shown to be asymptotically stable under a class of delayed replicator dynamics.