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arXiv · 1908.06266

Generalized potential games

M. H. Duong·T. H. Dang-Ha·Q. B. Tang·H. M. Tran
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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.

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BibTeXRIS

M. H. Duong, T. H. Dang-Ha, Q. B. Tang, H. M. Tran. 2019-08-17. Generalized potential games. https://arxiv.org/abs/1908.06266

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