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Dynamic spectrum leasing (DSL) was proposed recently as a new paradigm for dynamic spectrum sharing (DSS) in cognitive radio networks (CRN's). In this paper, we propose a new way to encourage primary users to lease their spectrum: The secondary users (SU's) place bids indicating how much power they are willing to spend for relaying the primary signals to their destinations. In this formulation, the primary users achieve power savings due to asymmetric cooperation. We propose and analyze both a centralized and a distributed decision-making architecture for the secondary CRN. In the centralized architecture, a Secondary System Decision Center (SSDC) selects a bid for each primary channel based on optimal channel assignment for SU's. In the decentralized cognitive network architecture, we formulate an auction game-based protocol in which each SU independently places bids for each primary channel and receivers of each primary link pick the bid that will lead to the most power savings. A simple and robust distributed reinforcement learning mechanism is developed to allow the users to revise their bids and to increase their rewards. The performance results show the significant impact of reinforcement learning in both improving spectrum utilization and meeting individual SU performance requirements.