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When electricity becomes deregulated, the price of electricity is not determined by a regulatory authority but by market demand, supply conditions, and strategic behavior. 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. The market, however, is subject to both supply and demand side uncertainties. This paper provides analytical models and procedures based on generation system and load data for probabilistically representing two different market competition models — one is based on perfect competition and the other based on asymmetric oligopoly (Cournot). We account for the availability of generating units and show its effects on market prices. We also study the effects on a firm´s expected profit when generator availabilities are neglected in the offers decisions. A numerical example is given for an electricity market for which the expected duration curve of the Nash-equilibrium electricity price as well as the mean of the individual firms´ profits are calculated. The effects of unit commitment, transmission congestion, and transmission outages are not considered.