Passivity and Evolutionary Game Dynamics

TL;DR

This paper explores the passivity property in evolutionary game dynamics, linking energy conservation principles to stability analysis, and provides systematic methods for examining passivity in such models.

Contribution

It introduces a formal notion of passivity for evolutionary game models and develops systematic methods to analyze their stability properties.

Findings

Passivity relates to stability in population games.

Passive models exhibit stable dynamics in simulations.

Systematic methods for passivity analysis are proposed.

Abstract

This paper investigates an energy conservation and dissipation -- passivity -- aspect of dynamic models in evolutionary game theory. We define a notion of passivity using the state-space representation of the models, and we devise systematic methods to examine passivity and to identify properties of passive dynamic models. Based on the methods, we describe how passivity is connected to stability in population games and illustrate stability of passive dynamic models using numerical simulations.