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On spectrum sharing games

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Abstract

Efficient spectrum-sharing mechanisms are crucial to alleviate the bandwidth limitation in wireless networks. In this paper, we consider the following question: can free spectrum be shared efficiently? We study this problem in the context of 802.11 or WiFi networks. 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 (i.e., not in a coordinated way) 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 optimally 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.

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Authors and Affiliations

  1. School of Computer Science, Reykjavik University, 101, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Department of Computer Science, Cornell University, Ithaca, NY, 14853, USA

    Joseph Y. Halpern

  3. Center for Networking Research, Bell Labs, Alcatel-Lucent, Murray Hill, NJ, 07974, USA

    Li Erran Li

  4. Theory Group, Google Research, New York, NY, USA

    Vahab S. Mirrokni

Authors
  1. Magnús M. Halldórsson
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  2. Joseph Y. Halpern
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  3. Li Erran Li
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  4. Vahab S. Mirrokni
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Correspondence to Li Erran Li.

Additional information

A preliminary version of this paper appeared in ACM Symposium on Principles of Distributed Computing(PODC), 2004.

Halpern’s work was supported in part by NSF under grant CTC-0208535, by ONR under grants N00014-00-1-03-41 and N00014-01-10-511, by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the ONR under grant N00014-01-1-0795, and by AFOSR under grant F49620-02-1-0101. Li’s work was partially supported by NSF ANI-0335244.

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Halldórsson, M.M., Halpern, J.Y., Li, L.E. et al. On spectrum sharing games. Distrib. Comput. 22, 235–248 (2010). https://doi.org/10.1007/s00446-010-0098-0

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