Singleton spectrum mobility games with incomplete information

In cognitive radio networks (CRNs), Secondary Users (SUs) are provided opportunities to access Primary Users´ (PUs´) idle spectrums but the availability of spectrums is dynamic due to PUs´ uncertain activities of channel reclamation. In this paper, we investigate such spectrum mobility by proposing Singleton Bayesian Spectrum Mobility Games based on the Singleton Congestion Games, where each SU distributively reselects one switch-to (and available) channel which can bring it the maximum SINR when the spectrum environment varies, accounting for other SUs´ switching strategies at the same time. Unlike previous game-theoretic schemes for handling the spectrum mobility that assume SUs´ complete knowledge of the CRN, we present our scheme in two information scenarios. We first demonstrate the proposed game in the complete-information scenario and prove the existence of pure Nash equilibriums. Then the game is extended to the incomplete-information scenario with the existence of Bayesian equilibriums. Besides, the other major contribution of this paper is that we provide a polynomial-time algorithm for finding the socially optimal equilibrium among all possible equilibriums, which can optimize the (expected) overall performance of the entire CRN in terms of SUs´ average SINR.