Spectrum allocation from a game theoretic perspective: Properties of Nash equilibria

We consider a scenario consisting of two transmit-receive pairs coexisting in the same area and communicating using the same portion of the spectrum. Applying a game theoretic framework, each pair is regarded as a player whose payoff function is the individual link rate and power is allocated using the iterative water-filling algorithm. We study the dynamics of such a game and find properties of the resulting Nash equilibria. For high interference scenarios, operating points admitting complete, partial or no overlap are possible and we present conditions under which the different Nash equilibria are achievable. Based on this analysis, a modified water-filling algorithm is designed to increase the sum-rate of the communication links. Its performance is compared to that of the iterative water-filling algorithm by numerical simulations. Although we restrict the analysis to a two player game, analogous concepts can be used to design decentralized algorithms for scenarios with more players.