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A new approach to unit maintenance scheduling (UMS) problems in competitive electricity markets is presented in this paper. The objectives of this study are to develop a new framework for UMS in competitive markets, to analyze a strategic behavior of profit maximizing generating companies (Gencos) in an UMS game, and to discuss equilibriums of the game from the standpoint of whole generation market. We have applied game theory to formulate the UMS problem as a dynamic noncooperative game. The players are profit maximizing privatized Gencos and the payoffs of each player have been defined as the profits from energy markets. All the players have been encouraged to maximize their profits, competing with each other. Strategic behaviors of individual Genco and corresponding Nash equilibrium of the UMS game were analyzed using a numerical example for two-player game. The results indicate that unit maintenance schedules are one of the major strategic behaviors whereby Gencos maximize their profits in a competitive market environment and that it should be dealt with more elaborately in viewpoints of privatized Gencos as well as whole market.