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Rosenthal's potential and a discrete version of the Debreu--Gorman Theorem

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  • Kukushkin, Nikolai S.

Abstract

The acyclicity of individual improvements in a generalized congestion game (where the sums of local utilities are replaced with arbitrary aggregation rules) can be established with a Rosenthal-style construction if aggregation rules of all players are "quasi-separable." Every universal separable ordering on a finite set can be represented as a combination of addition and lexicography.

Suggested Citation

  • Kukushkin, Nikolai S., 2014. "Rosenthal's potential and a discrete version of the Debreu--Gorman Theorem," MPRA Paper 54171, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:54171
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    File URL: https://mpra.ub.uni-muenchen.de/54171/1/MPRA_paper_54171.pdf
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    References listed on IDEAS

    as
    1. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
    2. Nikolai Kukushkin, 2007. "Congestion games revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 57-83, September.
    3. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    4. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, September.
    5. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    6. W. M. Gorman, 1968. "The Structure of Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 367-390.
    7. Sandholm, William H., 2010. "Decompositions and potentials for normal form games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 446-456, November.
    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. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
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    Cited by:

    1. Kukushkin, Nikolai, 2019. "Quasiseparable aggregation in games with common local utilities," MPRA Paper 93588, University Library of Munich, Germany.

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    More about this item

    Keywords

    Improvement dynamics; Acyclicity; Separable aggregation; Congestion game;
    All these keywords.

    JEL classification:

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

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