Decentralized spectrum access via multivariate global games

We consider a network of cognitive radios (CRs) where each CR obtains noisy multivariate measurements of the quality of several logical channels and needs to decide which channel to access. Assuming the CRs are rational devices, each CR determines which channel to access, based on its expected throughput and Bayesian estimate of the intention of other CRs. We formulate conditions for which the Bayesian Nash equilibrium of the resulting global game is monotonically increasing in the quality of the logical channel. This leads to a simple characterization of the competitive optimal behavior of the system as a function of the prior probability distribution of spectrum hole occupancy, channel quality and observation noise.