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Cognitive radio (CR) enabled dynamic spectrum access (DSA) networks are designed to detect and opportunistically utilise the unused or under-utilised spectrum bands. However, due to the open paradigm of CR networks and lack of proactive security protocols, the DSA networks are vulnerable to various denial-of-service threats. The authors propose a game-theoretic framework to study the primary user emulation attack (PUEA) on CR nodes. A non-cooperative dynamic multistage game between the secondary nodes and the adversaries generating the PUEA is formulated. The pure-strategy and mixed-strategy Nash equilibria for the secondary user and malicious attacker are investigated. Moreover, a novel belief updating system is proposed for the secondary user to learn the state of the primary user as the game evolves. Simulation results demonstrate that the proposed belief updating system achieves better performance than other models for the secondary user in terms of greater payoff, lower probability of missing primary user and better robustness to the inaccurate estimation of the primary user's state.