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We recently proposed the dynamic spectrum leasing (DSL) paradigm for dynamic spectrum access in cognitive radio networks. In this paper, we formalize this concept by developing a general game-theoretic framework for the DSL and by carefully identifying requirements for the coexistence of primary and secondary systems via spectrum leasing. In contrast to hierarchical spectrum access, spectrum owners in proposed DSL networks, which are denoted as primary users, dynamically adjust the amount of secondary interference that they are willing to tolerate in response to the demand from secondary transmitters. The secondary transmitters, in turn, opportunistically attempt to achieve maximum possible throughput, or another suitably defined reward, while not violating the interference limit that is set by the primary users. The new game-theoretic model, however, allows the secondary users to encourage the spectrum owners to push the interference cap upward based on demand. We have proposed a general structure for the utility functions of primary users and secondary users that allows the primary users to control the price and the demand for spectrum access based on their required quality of service (QoS). We establish that, with these utility functions, the DSL game has a unique Nash equilibrium to which the best response adaptation finally converges. Moreover, it is shown that the proposed coexistence and best response adaptations can be achieved with no significant interaction between the two systems. In fact, it is shown that the only requirement is that the primary system periodically broadcasts two parameter values. We use several examples to illustrate the system behavior at the equilibrium and use the performance at the equilibrium to identify suitable system design parameters.