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On the performances of Nash equilibria in isolation games

Author

Listed:
  • Vittorio Bilò

    (Università del Salento)

  • Michele Flammini

    (Università di L’Aquila)

  • Gianpiero Monaco

    (INRIA/CNRS/UNSA)

  • Luca Moscardelli

    (Università di Chieti-Pescara)

Abstract

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.

Suggested Citation

  • Vittorio Bilò & Michele Flammini & Gianpiero Monaco & Luca Moscardelli, 2011. "On the performances of Nash equilibria in isolation games," Journal of Combinatorial Optimization, Springer, vol. 22(3), pages 378-391, October.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:3:d:10.1007_s10878-010-9300-3
    DOI: 10.1007/s10878-010-9300-3
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    References listed on IDEAS

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    1. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 27-49.
    2. H. A. Eiselt & Gilbert Laporte & Jacques-François Thisse, 1993. "Competitive Location Models: A Framework and Bibliography," Transportation Science, INFORMS, vol. 27(1), pages 44-54, February.
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    Cited by:

    1. Anna Angelucci & Vittorio Bilò & Michele Flammini & Luca Moscardelli, 2015. "On the sequential price of anarchy of isolation games," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 165-181, January.
    2. Jasper Jong & Marc Uetz, 2020. "The quality of equilibria for set packing and throughput scheduling games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 321-344, March.

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