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A Spatial Game for Access Points Placement in Cognitive Radio Networks with Multi-Type Service

This paper studies the problem of determining locations of Secondary Access Points (SAPs) which belong to two competitive service providers in a certain region. SUs connect to the SAP according to their preferences. A key feature of our modeling approach is that it permits SAPs to set \textit{discriminatory powers} for SUs, that is, SUs in different locations will be scheduled with different transmission powers. The 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 the 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. An example demonstrating how to place SAPs in a linear region is presented.