On the Performances of Nash Equilibria in Isolation Games

  • Vittorio Bilò
  • Michele Flammini
  • Gianpiero Monaco
  • Luca Moscardelli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5609)


We study the performances of Nash equilibria in isolation games, a class of competitive location games recently introduced in [14]. For all the cases in which the existence of Nash equilibria has been shown, we give tight or asymptotically tight bounds on the prices of anarchy and stability under the two classical social functions mostly investigated in the scientific literature, namely, the minimum utility per player and the sum of the players’ utilities. Moreover, we prove that the convergence to Nash equilibria is not guaranteed in some of the not yet analyzed cases.


Nash Equilibrium Weight Vector Social Function Social Optimum Tight Bound 
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  1. 1.
    Ahn, H.K., Cheng, S.W., Cheong, O., Golin, M.J., Oostrum, R.: Competitive facility location: the Voronoi game. Theoretical Computer Science 310(1-3), 457–467 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Anshelevich, E., Dasgupta, A., Tardos, E., Wexler, T.: Near-Optimal Network Design with Selfish Agents. In: Proc. of the 35th Annual ACM Symposium on Theory of Computing (STOC), pp. 511–520. ACM Press, New York (2003)Google Scholar
  3. 3.
    Cheong, O., Har-Peled, S., Linial, N., Matousek, J.: The one-round Voronoi game. Discrete and Computational Geometry 31, 125–138 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dürr, C., Thang, N.K.: Nash equilibria in Voronoi games on graphs. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 17–28. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Eaton, B.C., Lipsey, R.G.: The principle of minimum differentiation reconsidered: Some new developments in the theory of spatial competition. Review of Economic Studies 42(129), 27–49 (1975)CrossRefzbMATHGoogle Scholar
  6. 6.
    Eiselt, H.A., Laporte, G., Thisse, J.F.: Competitive location models: A framework and bibliography. Transportation Science 27(1), 44–54 (1993)CrossRefzbMATHGoogle Scholar
  7. 7.
    Fekete, S.P., Meijer, H.: The one-round Voronoi game replayed. Computational Geometry: Theory and Applications 30, 81–94 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hotelling, H.: Stability in competition. Computational Geometry: Theory and Applications 39(153), 41–57 (1929)Google Scholar
  9. 9.
    Jain, A.K., Murty, M.N., Flynn, P.J.: Data Clustering: A Review. ACM Computing Surveys 31(3) (1999)Google Scholar
  10. 10.
    Koutsoupias, E., Papadimitriou, C.H.: Worst-Case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  11. 11.
    Mavronicolas, M., Monien, B., Papadopoulou, V.G., Schoppmann, F.: Voronoi games on cycle graphs. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 503–514. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Nash, J.: Equilibrium Points in n-Person Games. Proc. of the National Academy of Sciences 36, 48–49 (1950)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Teng, S.H.: Low Energy and Mutually Distant Sampling. Journal of Algorithms 30(1), 42–67 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Zhao, Y., Chen, W., Teng, S.H.: The Isolation Game: A Game of Distances. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 148–158. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Vittorio Bilò
    • 1
  • Michele Flammini
    • 2
  • Gianpiero Monaco
    • 2
  • Luca Moscardelli
    • 3
  1. 1.Dipartimento di Matematica “Ennio De Giorgi”Università del SalentoLecceItaly
  2. 2.Dipartimento di InformaticaUniversità di L’AquilaL’AquilaItaly
  3. 3.Dipartimento di ScienzeUniversità di Chieti-PescaraPescaraItaly

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