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Strong equilibrium in games with common and complementary local utilities

Author

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  • Kukushkin, Nikolai S.

Abstract

A rather general class of strategic games is described where the coalition improvements are acyclic and hence strong equilibria exist: The players derive their utilities from the use of certain "facilities"; all players using a facility extract the same amount of "local utility" therefrom, which amount depends both on the set of users and on their actions, and is decreasing in the set of users; the "ultimate" utility of each player is the minimum of the local utilities at all relevant facilities. Two important subclasses are "games with structured utilities," basic properties of which were discovered in 1970s and 1980s, and "bottleneck congestion games," which attracted researchers' attention quite recently. The former games are representative in the sense that every game from the whole class is isomorphic to one of them. The necessity of the minimum aggregation for the "persistent" existence of strong equilibria, actually, just Pareto optimal Nash equilibria, is established.

Suggested Citation

  • Kukushkin, Nikolai S., 2014. "Strong equilibrium in games with common and complementary local utilities," MPRA Paper 55499, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:55499
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    File URL: https://mpra.ub.uni-muenchen.de/55499/1/MPRA_paper_55499.pdf
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    References listed on IDEAS

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    1. Nikolai Kukushkin, 2007. "Congestion games revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 57-83, September.
    2. W. M. Gorman, 1968. "The Structure of Utility Functions," Review of Economic Studies, Oxford University Press, vol. 35(4), pages 367-390.
    3. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," Review of Economic Studies, Oxford University Press, vol. 44(2), pages 199-209.
    4. Deschamps, Robert & Gevers, Louis, 1978. "Leximin and utilitarian rules: A joint characterization," Journal of Economic Theory, Elsevier, vol. 17(2), pages 143-163, April.
    5. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    6. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January.
    7. Kukushkin, Nikolai S., 2008. "Maximizing an interval order on compact subsets of its domain," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 195-206, September.
    8. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    9. Kukushkin, Nikolai S, 1992. "On Existence of Stable and Efficient Outcomes in Games with Public and Private Objectives," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 295-303.
    10. 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.
    11. Smith, Tony E, 1974. "On the Existence of Most-Preferred Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 184-194, February.
    12. Nikolai Kukushkin, 2011. "Nash equilibrium in compact-continuous games with a potential," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 387-392, May.
    13. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    Cited by:

    1. Kukushkin, Nikolai S., 2018. "A universal construction generating potential games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 331-340.

    More about this item

    Keywords

    Strong equilibrium; Weakest-link aggregation; Coalition improvement path; Congestion game; Game with structured utilities;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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