Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Fundamentals of wireless communication
Fundamentals of wireless communication
Analysis of iterative waterfilling algorithm for multiuser power control in digital subscriber lines
EURASIP Journal on Applied Signal Processing
Algorithmic Game Theory
Power Control in Wireless Cellular Networks
Foundations and Trends® in Networking
Power control game in protected and shared bands: manipulability of Nash equilibrium
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Spectrum sharing games on the interference channel
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Resource allocation games in interference relay channels
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
High-SNR power offset in multiantenna communication
IEEE Transactions on Information Theory
Distributed multiuser power control for digital subscriber lines
IEEE Journal on Selected Areas in Communications
Spectrum sharing for unlicensed bands
IEEE Journal on Selected Areas in Communications
Convergence of Iterative Waterfilling Algorithm for Gaussian Interference Channels
IEEE Journal on Selected Areas in Communications
Competition Versus Cooperation on the MISO Interference Channel
IEEE Journal on Selected Areas in Communications
Competitive Design of Multiuser MIMO Systems Based on Game Theory: A Unified View
IEEE Journal on Selected Areas in Communications
Power control game in protected and shared bands: manipulability of Nash equilibrium
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Power allocation games in interference relay channels: existence analysis of nash equilibria
EURASIP Journal on Wireless Communications and Networking
Dynamic power allocation games in parallel multiple access channels
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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Motivated by the question, is non-cooperative spectrum sharing desirable or not, we consider a scenario utilizing protected and shared bands. In a static non-cooperative setting consisting of two communication system pairs, we study the existence, uniqueness and efficiency of a fixed point of the iterative water-filling algorithm which corresponds to the Nash equilibrium. There exist several sufficient conditions for the convergence of the algorithm in the literature mostly based on the contraction mapping theorem. We derive necessary and sufficient conditions for convergence by relating the game to supermodular games. There, the best response dynamics is globally convergent when a unique Nash equilibrium exists. In order to understand the loss in efficiency due to non-cooperation, we study the Price of Anarchy of the system. We show that the performance of the non-cooperative system cannot fall below two third of that of the cooperative system in the high signal to noise ratio regime. Theoretical results are illustrated by numerical simulations for a simplified system scenario.