Nash equilibrium as the minimum of a function. Application to electricity markets with large number of actors

We introduce in this paper a new approach for efficiently identifying Nash equilibria for games composed of large numbers of players having discrete and not too large strategy spaces. The approach is based on a characterization of Nash equilibria in terms of minima of a function and relies on stochastic optimization algorithms to find these minima. The approach is applied to compute Nash equilibria of some electricity markets and, based on the simulation results, its performances are discussed.