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Wind power is one of the most rapidly growing clean and renewable energy sources. However, due to the uncertainty and intermittency of wind power, the increasing penetration of wind power into the electric power system will pose challenges to power system operators. Moreover, as a participant in a competitive electricity market, a wind power producer's behavior and profit will be influenced by other participants' behaviors. This paper proposes a model of using stochastic programming to generate optimal bidding strategies to maximize the total profits of wind and conventional power producers in both the energy market and a bilateral reserve market, where the reserve price is settled between wind and conventional power producers by using game theory. Case studies using real-world data for games in an electricity market with different types of players are performed to show the effectiveness of the proposed model.