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This work investigates the diffusion of cooperative behavior over time in a decentralized cognitive radio network with selfish spectrum-sensing users. The users can individually choose whether or not to participate in cooperative spectrum sensing, in order to maximize their individual payoff defined in terms of the sensing false-alarm rate and transmit energy expenditure. The system is modeled as a partially connected network with a statistical distribution of the degree of the users, who play their myopic best responses to the actions of their neighbors at each iteration. Based on this model, we investigate the existence and characterization of Bayesian Nash Equilibria for the diffusion game. The impacts of network topology, channel fading statistics, sensing protocol, and multiple antennas on the outcome of the diffusion process are analyzed next. Simulation results that demonstrate how conducive different network scenarios are to the diffusion of cooperation are presented for further insight, and we conclude with a discussion on additional refinements and issues worth pursuing.