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Much of the research on bidding strategies in an electricity market has focused on idealized situations where participants have limited market power and the transmission system is not constrained. Yet, congestion may act to effectively give a bidder market power, and consequently the ability to influence the market clearing price. In such a noncompetitive situation, the bidding strategies of market participants will change. In this paper, the electrical power market is modeled as an oligopoly market and the Cournot quantity model is applied to the bidding strategy problem. The bidding process with congestion management is modeled as a three level optimization problem. A statistical methodology is then proposed as a solution for large systems.