Coordination Games on Graphs (Extended Abstract)

  • Krzysztof R. Apt
  • Mona Rahn
  • Guido Schäfer
  • Sunil Simon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8877)

Abstract

We introduce natural strategic games on graphs, which capture the idea of coordination in a local setting. We show that these games have an exact potential and have strong equilibria when the graph is a pseudoforest. We also exhibit some other classes of graphs for which a strong equilibrium exists. However, in general strong equilibria do not need to exist. Further, we study the (strong) price of stability and anarchy. Finally, we consider the problems of computing strong equilibria and of determining whether a joint strategy is a strong equilibrium.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. Games and Economic Behavior 65(2), 289–317 (2009)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Aumann, R.J.: Acceptable points in general cooperative n-person games. In: Luce, R.D., Tucker, A.W. (eds.) Contribution to the Theory of Game IV. Annals of Mathematical Study, vol. 40, pp. 287–324. University Press (1959)Google Scholar
  3. 3.
    Aziz, H., Brandl, F.: Existence of stability in hedonic coalition formation games. In: Proc. 11th International Conference on Autonomous Agents and Multiagent Systems, pp. 763–770 (2012)Google Scholar
  4. 4.
    Banerjee, S., Konishi: Core in a simple coalition formation game. Social Choice and Welfare 18(1), 135–153 (2001)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Bilò, V., Fanelli, A., Flammini, M., Moscardelli, L.: Graphical congestion games. Algorithmica 61(2), 274–297 (2011)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Bogomolnaia, A., Jackson, M.O.: The stability of hedonic coalition structures. Games and Economic Behavior 38(2), 201–230 (2002)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Cechlárová: Stable partition problem. In: Encyclopedia of Algorithms, pp. 885–888 (2008)Google Scholar
  8. 8.
    Gairing, M., Savani, R.: Computing stable outcomes in hedonic games. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 174–185. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Hoefer, M.: Cost sharing and clustering under distributed competition, Ph.D. Thesis, University of Konstanz (2007)Google Scholar
  10. 10.
    Janovskaya, E.: Equilibrium points in polymatrix games. Litovskii Matematicheskii Sbornik 8, 381–384 (1968)MATHMathSciNetGoogle Scholar
  11. 11.
    Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behaviour 14, 124–143 (1996)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Rozenfeld, O., Tennenholtz, M.: Strong and correlated strong equilibria in monotone congestion games. In: Spirakis, P., Mavronicolas, M., Kontogiannis, S. (eds.) WINE 2006. LNCS, vol. 4286, pp. 74–86. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Krzysztof R. Apt
    • 1
    • 2
  • Mona Rahn
    • 1
  • Guido Schäfer
    • 1
    • 3
  • Sunil Simon
    • 4
  1. 1.Centre for Mathematics and Computer Science (CWI)AmsterdamThe Netherlands
  2. 2.ILLCUniversity of AmsterdamThe Netherlands
  3. 3.VU University AmsterdamThe Netherlands
  4. 4.IIT KanpurKanpurIndia

Personalised recommendations