Ordinal potential functions for network selection in heterogeneous wireless networks

We consider the distributed allocation of spectrum in a heterogeneous wireless network. We model this as a noncooperative game, where multiple players decide which channels to transmit on. When co-channel interference between players is symmetric and channel utilities are additive, we define a generalized ordinal potential function for the game which is motivated by the energy function in Ising models. This guarantees convergence of best-response dynamics, and does not depend on the level of interference between players or on the price imposed on each channel.