Primal-dual evolutionary dynamics for constrained population games

TL;DR

This paper introduces a new primal-dual evolutionary dynamics framework for population games that incorporates constraints at equilibrium, extending traditional models and ensuring stability and feasibility through duality and Lyapunov methods.

Contribution

It proposes a novel primal-dual dynamics approach for constrained population games, enabling analysis of equilibrium stability and feasibility under constraints.

Findings

Established sufficient conditions for asymptotic stability of constrained equilibria.

Demonstrated the approach on classical population games with added constraints.

Ensured the feasibility of equilibria using duality and Lyapunov stability theories.

Abstract

Population games can be regarded as a tool to study the strategic interaction of a population of players. Although several attention has been given to such field, most of the available works have focused only on the unconstrained case. That is, the allowed equilibrium of the game is not constrained. To further extend the capabilities of population games, in this paper we propose a novel class of primal-dual evolutionary dynamics that allow the consideration of constraints that must be satisfied at the equilibrium of the game. Using duality theory and Lyapunov stability theory, we provide sufficient conditions to guarantee the asymptotic stability and feasibility of the equilibria set of the game under the considered constraints. Furthermore, we illustrate the application of the developed theory to some classical population games with the addition of constraints.