Journal of Combinatorial Optimization

, Volume 22, Issue 3, pp 378–391 | Cite as

On the performances of Nash equilibria in isolation games

  • Vittorio BilòEmail author
  • Michele Flammini
  • Gianpiero Monaco
  • Luca Moscardelli


We study the performances of Nash equilibria in isolation games, a class of competitive location games recently introduced in Zhao et al. (Proc. of the 19th International Symposium on Algorithms and Computation (ISAAC), pp. 148–159, 2008). 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 equilibria Price of anarchy and stability Isolation games 


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  1. Ahn HK, Cheng SW, Cheong O, Golin MJ, Oostrum R (2004) Competitive facility location: the Voronoi game. Theor Comput Sci 310(1–3):457–467 zbMATHCrossRefGoogle Scholar
  2. Anshelevich E, Dasgupta A, Tardos E, Wexler T (2003) Near-optimal network design with selfish agents. In: Proc of the 35th annual ACM symposium on theory of computing (STOC). ACM, New York, pp 511–520 Google Scholar
  3. Cheong O, Har-Peled S, Linial N, Matousek J (2004) The one-round Voronoi game. Discrete Comput Geom 31:125–138 MathSciNetzbMATHGoogle Scholar
  4. Dürr C, Thang NK (2007) Nash equilibria in Voronoi games on graphs. In: Proc of the 15th annual European symposium on algorithms (ESA). LNCS, vol 4698. Springer, Berlin, pp 17–28 Google Scholar
  5. Eaton BC, Lipsey RG (1975) The principle of minimum differentiation reconsidered: Some new developments in the theory of spatial competition. Rev Econ Stud 42(129):27–49 zbMATHGoogle Scholar
  6. Eiselt HA, Laporte G, Thisse JF (1993) Competitive location models: A framework and bibliography. Transp Sci 27(1):44–54 zbMATHCrossRefGoogle Scholar
  7. Fekete SP, Meijer H (2005) The one-round Voronoi game replayed. Comput Geom Theory Appl 30:81–94 MathSciNetzbMATHGoogle Scholar
  8. Hotelling H (1929) Stability in competition. Comput Geom Theory Appl 39(153):41–57 Google Scholar
  9. Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31(3) Google Scholar
  10. Koutsoupias E, Papadimitriou CH (1999) Worst-case equilibria. In: Proc of the 16th international symposium on theoretical aspects of computer science (STACS). LNCS, vol 1653. Springer, Berlin, pp 404–413 Google Scholar
  11. Mavronicolas M, Monien B, Papadopoulou VG, Schoppmann F (2008) Voronoi games on cycle graphs. In: Proc. of the 33rd international symposium on mathematical foundations of computer science (MFCS). LNCS, vol 5162. Springer, Berlin, pp 503–514 Google Scholar
  12. Nash J (1950) Equilibrium points in n-person games. In: Proc of the national academy of sciences, vol 36, pp 48–49 Google Scholar
  13. Teng SH (1999) Low energy and mutually distant sampling. J Algorithms 30(1):42–67 CrossRefGoogle Scholar
  14. Zhao Y, Chen W, Teng SH (2008) The isolation game: A game of distances. In: Proc of the 19th international symposium on algorithms and computation (ISAAC). LNCS, vol 5369. Springer, Berlin, pp 148–159 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Vittorio Bilò
    • 1
    Email author
  • Michele Flammini
    • 2
  • Gianpiero Monaco
    • 3
  • Luca Moscardelli
    • 4
  1. 1.Dipartimento di Matematica “Ennio De Giorgi”Università del SalentoLecceItaly
  2. 2.Dipartimento di InformaticaUniversità di L’AquilaCoppito, L’AquilaItaly
  3. 3.Mascotte joint projectINRIA/CNRS/UNSASophia AntipolisFrance
  4. 4.Dipartimento di ScienzeUniversità di Chieti-PescaraPescaraItaly

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