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In this paper, we propose a novel Nash problem for cognitive radio (CR) networks wherein each secondary user (player) aims to maximize his own opportunistic throughput by choosing jointly the sensing duration, the detection thresholds, and the power allocation over a multichannel link. The formulation contains constraints on the transmit power (and possibly spectral masks) as well as (probabilistic) average interference tolerable at the primary receivers. A new decision model for energy detectors that is robust against device-level uncertainties and system-level uncertainties is also proposed. The resulting players' optimization problems are nonconvex, which presents a new challenge for the analysis of this class of Nash games that cannot be addressed using mathematical tools from the game theory literature. To deal with the nonconvexity of the game, we introduce new relaxed equilibrium concepts, the Quasi-Nash Equilibrium (QNE) and Local Nash Equilibrium (LNE) and study the main properties of these equilibria, their connection, and their performance. Quite interestingly, the proposed joint optimization of the sensing and transmission parameters is shown to yield a considerable performance improvement with respect to current designs of CR systems, which validates the proposed new concept of QNE.