In this paper, we study the competition among the primary users (PUs) in a Dynamic Spectrum Leasing (DSL) system where multiple PUs lease spectrum to the secondary users (SUs) for monetary rewards. Considering the uncertainties of the PUs' channel gains and of the SUs' demands for spectrum, the competition among the PUs is formulated as a stochastic Nash game. Due to the uncertainties, the PUs aim to maximize their long term utilities which are related to the income from leasing spectrum and to their quality of service(QoS) conditions. Resorting to the stochastic variational inequality (SVI) theory, we investigate the existence and uniqueness of the stochastic Nash equilibrium (SNE). Based on the stochastic approximation theory, we propose a distributed learning algorithm for computing the SNE of the game. Rigorous convergence proof of the algorithm is provided. Besides, the features of the algorithm are demonstrated via numerical results.
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