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Cognitive radio is emerging as a promising technique to improve the utilization of radio frequency spectrum. In this paper, the authors consider the problem of spectrum sharing among primary (or "Licensed") and secondary (or "Unlicensed") users. They formulate the problem based on bandwidth auction in which each secondary user makes a bid for the amount of spectrum and each primary user may assign the spectrum among secondary users by itself according to the information from secondary users without degrading its own performance. They show that the auction is a non-cooperative game and Nash equilibrium can be its solution. They first consider a single-primary-user network to investigate the existence and uniqueness of Nash equilibrium, and further discuss the fairness among secondary users under given conditions.
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