Generalized potential games

TL;DR

This paper introduces generalized potential games inspired by gradient flow theory, applies it to chemical reaction networks, and proves exponential convergence to equilibrium with supporting numerical results.

Contribution

It defines a new class of generalized potential games and demonstrates their properties and applications in chemical reaction networks.

Findings

Exponential convergence to equilibrium in reversible reactions

Numerical methods for equilibrium calculation

Application to chemical reaction networks

Abstract

In this paper, we introduce a notion of generalized potential games that is inspired by a newly developed theory on generalized gradient flows. More precisely, a game is called generalized potential if the simultaneous gradient of the loss functions is a nonlinear function of the gradient of a potential function. Applications include a class of games arising from chemical reaction networks with detailed balance condition. For this class of games, we prove an explicit exponential convergence to equilibrium for evolution of a single reversible reaction. Moreover, numerical investigations are performed to calculate the equilibrium state of some reversible chemical reactions which give rise to generalized potential games.