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Because of nonstorability of electric energy, temporal effects are important in electricity markets. Demand fluctuation and generator outages cause stochastic behaviors in the market. Therefore, viewing the generation competition as a dynamic and stochastic game, rather than the traditional static deterministic game commonly considered in economics seems more appropriate. This paper studies the generator bidding using stochastic optimal control formulations. A stochastic and dynamic feedback system is proposed to model generation competition and then a stochastic optimal control problem is formulated to investigate individual's optimization behavior. With the proposed approach, two interesting issues are addressed: 1) what is the effect of generators' strategic behaviors on individual's payoffs, and 2) how market efficiency evolves with generators' strategic behavior. The result shows that that generators' strategic behaviors have positive effects on market efficiency and demonstrates that the evolution of individual's payoffs w.r.t. generators' strategic behavior resembles a game of "prisoner dilemma."