Distributional stability and deterministic equilibrium selection under heterogeneous evolutionary dynamics

TL;DR

This paper investigates how persistent payoff heterogeneity influences the evolution of strategies in heterogeneous populations, introducing a robust local stability concept and analyzing the effects of payoff sensitivity on evolutionary dynamics.

Contribution

It develops a stronger local stability concept for deterministic evolutionary dynamics under payoff heterogeneity and proposes tempered best response dynamics to parameterize payoff sensitivity.

Findings

Persistent payoff heterogeneity affects aggregate strategy evolution.

Homogenization occurs under standard best response dynamics.

Tempered best response dynamics capture payoff sensitivity effects.

Abstract

In the presence of persistent payoff heterogeneity, the evolution of the aggregate strategy hugely depends on the underlying strategy composition under many evolutionary dynamics, while the aggregate dynamic under the standard BRD reduces to a homogenized smooth BRD, where persistent payoff heterogeneity averages to homogeneous transitory payoff shocks. In this paper, we consider deterministic evolutionary dynamics in heterogeneous population and develop the stronger concept of local stability by imposing robustness to persistent payoff heterogeneity. It is known that nonaggregability holds generically if the switching rate in a given evolutionary dynamic correlates with the payoff gain from a switch. To parameterize the payoff sensitivity of an evolutionary dynamic, we propose to use tempered best response dynamics with bounded support of switching costs.