  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.
