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In this paper, an optimal bidding strategy of a generation company (GenCo's) that participates in a pay as bid electricity market is developed. A new method is proposed to obtain the Nash equilibrium point for optimal bidding strategy of GenCo's considering the risk of the bidding of the interested GenCo. For this purpose, the optimal bidding problem is modeled with two optimization sub-problems. In the first sub-problem, each GenCo maximizes its payoff, and in the second sub-problem, a system dispatch will be accomplished. particle swarm optimization (PSO) algorithm is used to find optimal bidding strategy of each GenCo in this method. For evaluating the risk of the bidding of the interested GenCo, appropriate range of the bidding of the GenCo is found such that the desired payoff is also achieved. The Western System Coordinating Council (WSCC) nine bus test system is used to illustrate the implementation of the proposed method for a typical power system.