Dynamic Pricing and Queue Stability in Wireless Random Access Games

We study the interaction among users of contention-based wireless networks, where the performance of the network is highly correlated with user transmission probabilities. Considering the underlying user incentives, we make use of the conceptual framework of noncooperative game theory to obtain a distributed control mechanism to limit the contention among wireless nodes by taking into account queue stability and injecting linear pricing to punish greedy behavior. We present a comprehensive analysis of the game including existence and uniqueness of Nash equilibrium point, convergence dynamics, and robustness properties. Utilizing linear pricing enables us to move the equilibrium point of the game to a desirable region. We obtain conditions on linear prices necessary to achieve stability of user queues in the asymmetric and symmetric cases. In addition, we propose dynamic pricing algorithms, in which wireless users play the game without cooperation while the base station adjusts the linear price of each user. Under limited knowledge of game parameters, we present a dynamic equal pricing algorithm that moves the Nash equilibrium to the aggregate throughput maximizing solution. The theoretical results are verified, and the convergence and efficiency of the proposed game are illustrated via simulations.

[1]  Lijun Chen,et al.  Random Access Game and Medium Access Control Design , 2010, IEEE/ACM Transactions on Networking.

[2]  Saurabh Ganeriwal,et al.  On selfish behavior in CSMA/CA networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[3]  Franklin F. Kuo,et al.  ALOHA packet broadcasting: a retrospect , 1975, AFIPS '75.

[4]  Cem U. Saraydar,et al.  Efficient power control via pricing in wireless data networks , 2002, IEEE Trans. Commun..

[5]  Rachid El Azouzi,et al.  A game theoretic approach for delay minimization in slotted ALOHA , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

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

[7]  Stephen B. Wicker,et al.  Stability of multipacket slotted Aloha with selfish users and perfect information , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[8]  Massimo Franceschetti,et al.  Cooperation in multi-access networks via coalitional game theory , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[9]  Eitan Altman,et al.  Slotted Aloha with Priorities and Random Power , 2005, NETWORKING.

[10]  George Kesidis,et al.  Equilibria of a noncooperative game for heterogeneous users of an ALOHA network , 2002, IEEE Communications Letters.

[11]  Tansu Alpcan,et al.  Noncooperative Games for Control of Networked Systems , 2006 .

[12]  Eitan Altman,et al.  Slotted Aloha as a game with partial information , 2004, Comput. Networks.

[13]  Demosthenis Teneketzis,et al.  A game-theoretic approach to decentralized optimal power allocation for cellular networks , 2008, Telecommun. Syst..

[14]  Stephen B. Wicker,et al.  Selfish users in Aloha: a game-theoretic approach , 2001, IEEE 54th Vehicular Technology Conference. VTC Fall 2001. Proceedings (Cat. No.01CH37211).

[15]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[16]  Tansu Alpcan,et al.  Nash equilibrium design and optimization , 2009, 2009 International Conference on Game Theory for Networks.

[17]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.