Multi-Channel Sensing and Access Game: Bayesian Social Learning with Negative Network Externality

In a distributed cognitive radio network, due to negative network externality, rational secondary users tend to avoid accessing the same vacant primary channels with others. Moreover, they usually need to make their channel access decisions in a sequential manner to avoid collisions. The characteristic of negative network externality and the structure of sequential decision making make the multi-channel sensing and access problem challenging, which has not been well studied by the existing literatures. To solve these problems, in this paper, we propose a multi-channel sensing and access game, which not only considers the negative network externality in secondary users´ decision making, but also takes into account their sequential decision making structure. We solve the multi-channel sensing problem using Bayesian learning method and design a cooperative learning rule for secondary users to accurately estimate the channel state. We study the multi-channel access problem under two scenarios: with and without resource constraint, respectively. For both scenarios, we design recursive best response algorithms for secondary users to find the subgame perfect Nash equilibria. Specifically, we analyze the homogenous case of the scenario without resource constraint and find that the Nash equilibrium profile exhibits a threshold structure. Finally, we conduct simulations to validate the effectiveness and efficiency of the proposed methods.