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This paper studies the problem of determining the locations of secondary access points (SAPs) that belong to two competitive service providers in a certain region. Secondary users (SUs) connect to SAPs according to their preferences. A key feature of the proposed model is that it permits SAPs to set discriminatory powers for SUs, i.e., SUs in different locations will be scheduled with different transmission powers. Profit-maximizing SAPs compete with each other by setting locations and delivered power schedules to attract SUs, taking into account the impact of the revenue obtained and the power cost incurred. To study this competitive situation, an appropriate extensive form game is defined. The game can be viewed as two-staged. The selection of transmission powers by SAPs can be investigated for each pair of locations. Then, the problem of location choice can be analyzed, anticipating what transmission powers will be chosen. We make an important observation: The Nash equilibrium of the game exists, and the global revenue maximum strategy is a Nash equilibrium strategy. Finally, we explore the equilibrium for a circular region having uniform SU distribution and illustrate how to locate SAPs for such a region.