STABILITY OF SOLUTIONS OF KINETIC EQUATIONS CORRESPONDING TO THE REPLICATOR DYNAMICS.

In the present paper we propose a class of kinetic type equations that describes the replicator dynamics at the mesoscopic level. The equations are highly nonlinear due to the dependence of the transition rates of distribution function. Under suitable assumptions we show the asymptotic (exponential) stability of the solutions to such kinetic equations. [ABSTRACT FROM AUTHOR]