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The Price of Anarchy for Network Formation in an Adversary Model

  • Lasse Kliemann

    ()

    (Department of Computer Science, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, Kiel 24098, Germany)

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    We study network formation with n players and link cost α > 0. After the network is built, an adversary randomly deletes one link according to a certain probability distribution. Cost for player ν incorporates the expected number of players to which ν will become disconnected. We focus on unilateral link formation and Nash equilibrium . We show existence of Nash equilibria and a price of stability of 1 + ο (1) under moderate assumptions on the adversary and n ≥ 9. We prove bounds on the price of anarchy for two special adversaries: one removes a link chosen uniformly at random, while the other removes a link that causes a maximum number of player pairs to be separated. We show an Ο (1) bound on the price of anarchy for both adversaries, the constant being bounded by 15 + ο (1) and 9 + ο (1), respectively.

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    Article provided by MDPI, Open Access Journal in its journal Games.

    Volume (Year): 2 (2011)
    Issue (Month): 3 (August)
    Pages: 302-332

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    Handle: RePEc:gam:jgames:v:2:y:2011:i:3:p:302-332:d:13673
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    1. Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer, vol. 38(1), pages 51-79, March.
    2. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    3. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    4. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
    5. Matthew O. Jackson & Francis Bloch, 2004. "The Formation of Networks with Transfers among Players," Working Papers 2004.80, Fondazione Eni Enrico Mattei.
    6. Johari, Ramesh & Mannor, Shie & Tsitsiklis, John N., 2006. "A contract-based model for directed network formation," Games and Economic Behavior, Elsevier, vol. 56(2), pages 201-224, August.
    7. Sudipta Sarangi & H. Haller, . "Nash Networks with Heterogeneous Agents," Departmental Working Papers 2003-06, Department of Economics, Louisiana State University.
    8. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
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