Strategic Behavior of Cognitive Radio Networks with Different Information

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The equilibrium joining probabilities for a single primary user (PU) and secondary users (SUs) in the case of no queue length information, and the equilibrium Nash balance thresholds for PU and SUs to join the system in the cases of partial queue length information and full queue length information observed by PU and SUs are investigated in a cognitive radio system. PU stochastically sends PU requests and each SU is assumed to only carry one SU request. Whenever a PU (or an SU) request is completed, a reward is issued to the PU (or the SU). However, a holding cost is charged also for each SU and PU during their average sojourn time in the system respectively. Both of PU requests and SU requests are selfish in this research and their objectives are to maximize their own benefit. Our major conclusion includes a threshold probability value for PU (or SU) to join the system identified for the case of no queue length information, a Nash balance PU (SU) threshold value is determined for the case of partial queue length information; and the multi-dimensional Nash balance threshold is established for the case of full queue length information. These Nash balance threshold integer values depend on not only the Nash Balance PU-threshold value but also the specific number of SU requests in the system at that arriving time. In addition, we discuss the sensibility of input parameters to the obtained equilibrium joining probabilities and Nash balance thresholds. We mathematically verify that SUs' equilibrium joining probability does not necessarily increase with the transmission rate of PU in no queue length information case and observe numerically that the Nash balance thresholds adopted by an arriving SU are fickle with the change of PU's transmission rate in both of partial and full queue length information cases. Our results and observations provide a guideline and important managerial insights in making decisions with strategic users in the design of CRNs.