Spectrum market stability and variation of rationality in a cognitive radio network

The transition to 5G and 6G presents spectrum dissipation challenges, requiring efficient utilization. Cognitive Radio Networks (CRNs) enable Primary Users (PUs) to lease unused spectrum to Secondary Users (SUs), which generates revenue while improving spectrum utilization efficiency. Consequently, PUs must manage their resources effectively while setting reasonable spectrum lease prices. To address this issue, this paper introduces a Cournot-type non-cooperative price game to model the selfish behavior of PUs under limited information driven by the dynamics of network. By employing a bounded rationality learning mechanism and a best-response algorithm, Nash Equilibrium (NE) is attained, allowing PUs to maximize profits autonomously and equitably while offering spectrum at competitive price rates—an increasingly vital goal as 5G/6G networks drive up spectrum demand and costs. In contrast to prior works that assumed fully rational behavior from all users at all times, a key contribution of this study is the examination of how variations in SU rationality over time affect system stability, reflecting the dynamic behavior of dense CRNs. Numerical simulations demonstrate that high learning rates, stringent QoS demands lead to chaotic and unstable dynamics, whereas lower irrationality contributes to price reduction. To mitigate instability, a time-delayed feedback control is applied to eliminate chaos and restore stability, offering key insights into user behavior and system efficiency for managing next-generation CRNs.