A stochastic Cournot model for market price of electricity

Several oligopoly models have been proposed for representing strategic behavior in electricity markets, notable among which is the Cournot model. The literature on this model has, for the most part, provided a deterministic treatment of the demand and supply side quantities. In this paper, we enhance this model by taking into account the uncertainties associated with load, generator availabilities, and marginal production costs. We obtain the Nash equilibrium solutions in which each firm submits its quantity bid such that its expected profit is maximized. As an illustration, a numerical example is given for an electricity market for which the mean and standard deviation of the equilibrium electricity price as well as the mean and standard deviation of the individual firms' profits are obtained.