Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution

TL;DR

This paper introduces a comprehensive framework for analyzing evolutionary dynamics in populations with arbitrary heterogeneity in types, payoff functions, and revision protocols, extending classical results to more complex, realistic scenarios.

Contribution

It develops a general mathematical framework for heterogeneous populations, establishing conditions for solution existence, equilibrium uniqueness, and stability, extending potential game results to heterogeneous settings.

Findings

Equilibrium stationarity and stability extend to heterogeneous populations.

A wide class of dynamics share stable equilibria via potential maximization.

Regularity conditions ensure unique solution trajectories.

Abstract

A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire joint distribution of strategies and types to influence the payoffs of agents. We clarify regularity conditions for the unique existence of a solution trajectory and for the existence of equilibrium. We confirm that equilibrium stationarity in general and equilibrium stability in potential games are extended from the homogeneous setting to the heterogeneous setting. In particular, a wide class of admissible dynamics share the same set of locally stable equilibria in a potential game through local maximization of the potential.