Asymptotic Optimality for Distributed Spectrum Sharing using Bargaining Solutions

Recent studies on spectrum usage reveal poor utilization, both spatially and temporally. Opportunistic use of licensed spectrum while limiting interference to primary users can enhance spectrum reuse and provide orders of magnitude improvement in available channel capacity. This calls for spectrum sharing protocols that are dynamic, flexible, and efficient, in addition to being fair to end users. We employ cooperative game theory to address the opportunistic spectrum access problem. Specifically, we develop a game-theoretic model to analyze a scenario in which nodes in a wireless network seek to agree on a fair and efficient allocation of spectrum. First, we show that in high interference environments, the utility space of the game is non-convex, making certain optimal allocations unachievable with pure strategies. To mitigate this, we show that as the number of channels available increases, the utility space approaches convexity, thereby making optimal allocations achievable with pure strategies. Second, by comparing and analyzing three bargaining solutions, we show that the Nash Bargaining Solution achieves the best tradeoff between fairness and efficiency, using a small number of channels. Finally, we develop a distributed algorithm for spectrum sharing that is general enough to accomodate non-zero disagreement points, and show that it achieves allocations reasonably close to the Nash Bargaining Solution.