Generalized potential games
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.
Keywords
Cite
@article{arxiv.1908.06266,
title = {Generalized potential games},
author = {M. H. Duong and T. H. Dang-Ha and Q. B. Tang and H. M. Tran},
journal= {arXiv preprint arXiv:1908.06266},
year = {2019}
}
Comments
23 pages, 6 figures. Comments are welcome