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Coordination games on graphs

Author

Listed:
  • Krzysztof R. Apt

    (Centrum Wiskunde & Informatica (CWI), Networks and Optimization Group)

  • Bart Keijzer

    (Centrum Wiskunde & Informatica (CWI), Networks and Optimization Group)

  • Mona Rahn

    (Centrum Wiskunde & Informatica (CWI), Networks and Optimization Group)

  • Guido Schäfer

    (Centrum Wiskunde & Informatica (CWI), Networks and Optimization Group
    Vrije Universiteit Amsterdam)

  • Sunil Simon

    (IIT Kanpur)

Abstract

We introduce natural strategic games on graphs, which capture the idea of coordination in a local setting. We study the existence of equilibria that are resilient to coalitional deviations of unbounded and bounded size (i.e., strong equilibria and k-equilibria respectively). We show that pure Nash equilibria and 2-equilibria exist, and give an example in which no 3-equilibrium exists. Moreover, we prove that strong equilibria exist for various special cases. We also study the price of anarchy (PoA) and price of stability (PoS) for these solution concepts. We show that the PoS for strong equilibria is 1 in almost all of the special cases for which we have proven strong equilibria to exist. The PoA for pure Nash equilbria turns out to be unbounded, even when we fix the graph on which the coordination game is to be played. For the PoA for k-equilibria, we show that the price of anarchy is between $$2(n-1)/(k-1) - 1$$ 2 ( n - 1 ) / ( k - 1 ) - 1 and $$2(n-1)/(k-1)$$ 2 ( n - 1 ) / ( k - 1 ) . The latter upper bound is tight for $$k=n$$ k = n (i.e., strong equilibria). Finally, we consider the problems of computing strong equilibria and of determining whether a joint strategy is a k-equilibrium or strong equilibrium. We prove that, given a coordination game, a joint strategy s, and a number k as input, it is co-NP complete to determine whether s is a k-equilibrium. On the positive side, we give polynomial time algorithms to compute strong equilibria for various special cases.

Suggested Citation

  • Krzysztof R. Apt & Bart Keijzer & Mona Rahn & Guido Schäfer & Sunil Simon, 2017. "Coordination games on graphs," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 851-877, August.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0560-8
    DOI: 10.1007/s00182-016-0560-8
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    References listed on IDEAS

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    1. Joseph T. Howson, Jr., 1972. "Equilibria of Polymatrix Games," Management Science, INFORMS, vol. 18(5-Part-1), pages 312-318, January.
    2. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    4. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    5. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    6. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    7. Tobias Harks & Max Klimm & Rolf Möhring, 2013. "Strong equilibria in games with the lexicographical improvement property," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 461-482, May.
    8. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
    9. Andelman, Nir & Feldman, Michal & Mansour, Yishay, 2009. "Strong price of anarchy," Games and Economic Behavior, Elsevier, vol. 65(2), pages 289-317, March.
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