On spectrum sharing games

Each access point (AP) in a WiFi network must be assigned a channel for it to service users. There are only finitely many possible channels that can be assigned. Moreover, neighboring access points must use different channels so as to avoid interference. Currently these channels are assigned by administrators who carefully consider channel conflicts and network loads. Channel conflicts among APs operated by different entities are currently resolved in an ad hoc manner or not resolved at all. We view the channel assignment problem as a game, where the players are the service providers and APs are acquired sequentially. We consider the price of anarchy of this game, which is the ratio between the total coverage of the APs in the worst Nash equilibrium of the game and what the total coverage of the APs would be if the channel assignment were done by a central authority. We provide bounds on the price of anarchy depending on assumptions on the underlying network and the type of bargaining allowed between service providers. The key tool in the analysis is the identification of the Nash equilibria with the solutions to a maximal coloring problem in an appropriate graph. We relate the price of anarchy of these games to the approximation factor of local optimization algorithms for the maximum k-colorable subgraph problem. We also study the speed of convergence in these games.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  Alexander Schrijver,et al.  On the Size of Systems of Sets Every t of Which Have an SDR, with an Application to the Worst-Case Ratio of Heuristics for Packing Problems , 1989, SIAM J. Discret. Math..

[3]  Harry B. Hunt,et al.  Simple heuristics for unit disk graphs , 1995, Networks.

[4]  Magnús M. Halldórsson,et al.  Approximating discrete collections via local improvements , 1995, SODA '95.

[5]  R. Ravi,et al.  Nonoverlapping Local Alignments (weighted Independent Sets of Axis-parallel Rectangles) , 1996, Discret. Appl. Math..

[6]  Dorit S. Hochba,et al.  Approximation Algorithms for NP-Hard Problems , 1997, SIGA.

[7]  Esther M. Arkin,et al.  On Local Search for Weighted k-Set Packing , 1998, Math. Oper. Res..

[8]  Christos H. Papadimitriou,et al.  Worst-case Equilibria , 1999, STACS.

[9]  J. Håstad Clique is hard to approximate withinn1−ε , 1999 .

[10]  Tim Roughgarden,et al.  How bad is selfish routing? , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[11]  Lars Engebretsen,et al.  Clique Is Hard To Approximate Within , 2000 .

[12]  Jon M. Peha,et al.  A novel co-existence algorithm for unlicensed fixed power devices , 2000, 2000 IEEE Wireless Communications and Networking Conference. Conference Record (Cat. No.00TH8540).

[13]  Berthold Vöcking,et al.  Selfish traffic allocation for server farms , 2002, STOC '02.

[14]  Omar Aftab,et al.  Economic mechanisms for efficient wireless coexistence , 2002 .

[15]  Adrian Vetta,et al.  Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[16]  Scott Shenker,et al.  On a network creation game , 2003, PODC '03.

[17]  Yishay Mansour,et al.  Convergence Time to Nash Equilibria , 2003, ICALP.

[18]  W. Kern,et al.  A new PTAS for maximum independent sets in unit disk graphs , 2003 .

[19]  Randeep Bhatia,et al.  MiFi: A framework for fairness and QoS assurance in current IEEE 802.11 networks with multiple access points , 2004, IEEE INFOCOM 2004.

[20]  Johann Hurink,et al.  A Robust PTAS for Maximum Weight Independent Sets in Unit Disk Graphs , 2004, WG.

[21]  Christos H. Papadimitriou,et al.  The complexity of pure Nash equilibria , 2004, STOC '04.

[22]  W. Kern,et al.  A robust PTAS for maximum independent sets in unit disk graphs , 2004 .

[23]  Vahab S. Mirrokni,et al.  Convergence Issues in Competitive Games , 2004, APPROX-RANDOM.

[24]  Srinivasan Seshan,et al.  Self-management in chaotic wireless deployments , 2005, MobiCom '05.

[25]  Suman Banerjee,et al.  Distributed channel management in uncoordinated wireless environments , 2006, MobiCom '06.

[26]  Michael L. Honig,et al.  Auction-Based Spectrum Sharing , 2006, Mob. Networks Appl..

[27]  Jean-Pierre Hubaux,et al.  Wireless Operators in a Shared Spectrum , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[28]  Marina Thottan,et al.  Market sharing games applied to content distribution in ad hoc networks , 2004, IEEE Journal on Selected Areas in Communications.

[29]  Y. Bejerano,et al.  MiFi: a framework for fairness and QoS assurance for current IEEE 802.11 networks with multiple access points , 2006, IEEE/ACM Transactions on Networking.