Quality of Service Games for Spectrum Sharing

Today's wireless networks are increasingly crowded with an explosion of wireless users, who have greater and more diverse quality of service (QoS) demands than ever before. However, the amount of spectrum that can be used to satisfy these demands remains finite. This leads to a great challenge for wireless users to effectively share the spectrum to achieve their QoS requirements. This paper presents a game theoretic model for spectrum sharing, where users seek to satisfy their QoS demands in a distributed fashion. Our spectrum sharing model is quite general, because we allow different wireless channels to provide different QoS, depending upon their channel conditions and how many users are trying to access them. Also, users can be highly heterogeneous, with different QoS demands, depending upon their activities, hardware capabilities, and technology choices. Under such a general setting, we show that it is NP hard to find a spectrum allocation which satisfies the maximum number of users' QoS requirements in a centralized fashion. We also show that allowing users to self-organize through distributed channel selections is a viable alternative to the centralized optimization, because better response updating is guaranteed to reach a pure Nash equilibria in polynomial time. By bounding the price of anarchy, we demonstrate that the worst case pure Nash equilibrium can be close to optimal, when users and channels are not very heterogenous. We also extend our model by considering the frequency spatial reuse, and consider the user interactions as a game upon a graph where players only contend with their neighbors. We prove that better response updating is still guaranteed to reach a pure Nash equilibrium in this more general spatial QoS satisfaction game.