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Cognitive Radio (CR) is a next-generation wireless communication system that exploits underutilized licensed spectrum to optimize the utilization of the overall radio spectrum. A Distributed Cognitive Radio Network (DCRN) is a distributed wireless network established by a number of CR hosts in the absence of fixed network infrastructure. Context-awareness and intelligence are key characteristics of CR networks that enable the CR hosts to be aware of their operating environment in order to make an efficient and optimal joint action. Applying our extended Payoff Propagation (PP) mechanism in DCRN helps the CR hosts to achieve an efficient and optimal joint action in a cooperative and distributed manner through learning. The PP is suitable to be applied in most schemes in DCRN that requires context-awareness and intelligence such as Dynamic Channel Selection (DCS), scheduling, and congestion control. We investigate the performance of the PP in respect to DCS, and show that it is able to converge to an efficient and optimal joint action in a distributed manner including a DCRN with cyclic topology; furthermore we show that fast convergence is possible.