In this paper, a mechanism for spectrum allocation in overlay cognitive radio networks is proposed. In overlay cognitive radio networks, the secondary users (SUs) must first sense the activity of primary users (PUs) to identify unoccupied spectrum bands. Based on their different contributions for the spectrum sensing, the SUs get payoffs that are computed by the fusion center (FC). The unoccupied bands will be auctioned and SUs are asked to bid using payoffs they earned or saved. Coalitions are allowed to form among SUs because each SU may only need a portion of the bands. We formulate the coalition forming process as a coalition forming game and analyze it by game theory. In the coalition formation game, debtor-creditor relationship may occur among the SUs because of their limited payoff storage. A debtor asks a creditor for payoff help, and in return provides the creditor with a portion of transmission time to relay data for the creditor. The negotiations between debtors and creditors can be modeled as a Bayesian game because they lack complete information of each other, and the equilibria of the game is investigated. Theoretical analysis and numerical results show that the proposed auction yields data rate improvement and certain fairness among all SUs.
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