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The authors study the pricing issue in a competitive cognitive radio network in which the secondary users strategically adjust their uplink transmission power levels to maximize their own utilities, and the primary service provider (e.g., base station) charges the secondary users on their transmitted power levels to enhance its own revenue. They model the competitive behavior of the secondary users as a non-cooperative game and address the existence and uniqueness of Nash equilibrium. Based on the unique equilibrium, they formulate the pricing problem for the primary service provider as a non-convex optimization problem.
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