K-player Bayesian waterfilling game for fading multiple access channels

We present a Bayesian game-theoretic approach for the distributed resource allocation problem in the context of K-user fading multiple access channels (MAC). We assume that users have incomplete information about the channel state information (CSI), i.e., each user knows his own channel state, but does not know the states of other users. All users (transmitters) are considered to be rational, selfish, and each one carries the objective of maximizing its own achievable data rate. In such a game-theoretic study, the central question is whether a Bayesian equilibrium (BE) exists. Based on the assumption of two channel states, we prove that there exists exactly one BE in this game.

[1]  David Tse,et al.  Multiaccess Fading Channels-Part I: Polymatroid Structure, Optimal Resource Allocation and Throughput Capacities , 1998, IEEE Trans. Inf. Theory.

[2]  Heikkinen Tiina A Minimax Game of Power Control in a Wireless Network under Incomplete Information , 1999 .

[3]  S. Lasaulce,et al.  Methodologies for analyzing equilibria in wireless games , 2009, IEEE Signal Process. Mag..

[4]  Sergio Verdú,et al.  Gaussian multiaccess channels with ISI: Capacity region and multiuser water-filling , 1993, IEEE Trans. Inf. Theory.

[5]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[6]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Andrea J. Goldsmith,et al.  Competition in Wireless Systems via Bayesian Interference Games , 2007, ArXiv.

[8]  B. Jabbari,et al.  Bayesian game-theoretic modeling of transmit power determination in a self-organizing CDMA wireless network , 2004, IEEE 60th Vehicular Technology Conference, 2004. VTC2004-Fall. 2004.

[9]  Raymond Knopp,et al.  Information capacity and power control in single-cell multiuser communications , 1995, Proceedings IEEE International Conference on Communications ICC '95.

[10]  Hesham El Gamal,et al.  The Water-Filling Game in Fading Multiple-Access Channels , 2005, IEEE Transactions on Information Theory.

[11]  J. Goodman Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[12]  Mérouane Debbah,et al.  Game-theoretic deployment design of small-cell OFDM networks , 2009, VALUETOOLS.

[13]  M. Dufwenberg Game theory. , 2011, Wiley interdisciplinary reviews. Cognitive science.

[14]  M. Debbah,et al.  Mobile Flexible Networks: The challenges ahead , 2008, 2008 International Conference on Advanced Technologies for Communications.

[15]  Pravin Varaiya,et al.  Capacity of fading channels with channel side information , 1997, IEEE Trans. Inf. Theory.

[16]  Mérouane Debbah,et al.  Power allocation games for mimo multiple access channels with coordination , 2009, IEEE Transactions on Wireless Communications.

[17]  Eitan Altman,et al.  Game Theoretic approach for routing in dense ad-hoc networks , 2007 .

[18]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.