On the stability of monotone discrete selection dynamics with inertia

Abstract

In this paper we study the learning behavior of a population of boundedly rational players who interact by repeatedly playing an evolutionary game. A simple imitation type learning rule for the agents is suggested and it is shown that the evolution of the population strategy is described by the discrete time replicator dynamics with inertia. Conditions are derived which guarantee the local stability of a Nash-equilibrium with respect to these dynamics and for quasi-strict ESS with support of three pure strategies the crucial level of inertia is derived which ensures stability and avoids overshooting. These results are illustrated by an example and generalized to the class of monotone selection dynamics.