Game theoretic aspects of the multi-channel ALOHA protocol in cognitive radio networks

In this paper we consider the problem of distributed throughput maximization of cognitive radio networks with the multi-channel ALOHA medium access protocol. First, we characterize the Nash Equilibrium Points (NEPs) of the network when users solve an unconstrained rate maximization (i.e., the total transmission probability equals one). Then, we focus on constrained rate maximization, where user rates are subject to a total transmission probability constraint. We propose a simple best-response algorithm that solves the constrained rate maximization, where each user updates its strategy using its local channel state information (CSI) and by monitoring the channel utilization. We prove the convergence of the proposed algorithm using the theory of potential games. Furthermore, we show that the network approaches a unique equilibrium as the number of users increases. Then, we formulate the problem of choosing the access probability as a leader-followers Stackelberg game, where a single user is chosen to be the leader to manage the network. We show that a fully distributed setup can be applied to approximately optimize the network throughput for a large number of users. Finally, we extend the model to the case where primary and secondary users co-exist in the same frequency band.