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A universal construction generating potential games

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  • Kukushkin, Nikolai S.

Abstract

Strategic games are considered where each player's total utility is the sum of local utilities obtained from the use of certain “facilities.” All players using a facility obtain the same utility therefrom, which may depend on the identities of users and on their behavior. If a “trimness” condition is satisfied by every facility, then the game admits an exact potential; conversely, if a facility is not trim, adding it to a potential game may destroy that property. In both congestion games and games with structured utilities, all facilities are trim. Under additional assumptions the potential attains its maximum, which is a Nash equilibrium of the game.

Suggested Citation

  • Kukushkin, Nikolai S., 2018. "A universal construction generating potential games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 331-340.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:331-340
    DOI: 10.1016/j.geb.2017.02.012
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    References listed on IDEAS

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    1. Mark Voorneveld & Peter Borm & Freek Van Megen & Stef Tijs & Giovanni Facchini, 1999. "Congestion Games And Potentials Reconsidered," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 283-299.
    2. Nikolai Kukushkin, 2007. "Congestion games revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 57-83, September.
    3. 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.
    4. Le Breton, Michel & Weber, Shlomo, 2011. "Games of social interactions with local and global externalities," Economics Letters, Elsevier, vol. 111(1), pages 88-90, April.
    5. Nikolai S Kukushkin, 2004. "'Strategic supplements' in games with polylinear interactions," Game Theory and Information 0411008, University Library of Munich, Germany, revised 28 Feb 2005.
    6. Kukushkin, Nikolai S., 2017. "Strong Nash equilibrium in games with common and complementary local utilities," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 1-12.
    7. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    8. Kukushkin, Nikolai S., 2014. "Strong equilibrium in games with common and complementary local utilities," MPRA Paper 55499, University Library of Munich, Germany.
    9. 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.
    10. repec:fth:tilbur:9998 is not listed on IDEAS
    11. 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, 2019. "Quasiseparable aggregation in games with common local utilities," MPRA Paper 93588, University Library of Munich, Germany.
    2. Gusev, Vasily V., 2021. "Nash-stable coalition partition and potential functions in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1180-1188.
    3. Nikolai S. Kukushkin, 2017. "Inseparables: exact potentials and addition," Economics Bulletin, AccessEcon, vol. 37(2), pages 1176-1181.

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    More about this item

    Keywords

    Potential game; Congestion game; Game with structured utilities; Game of social interactions; Additive aggregation;
    All these keywords.

    JEL classification:

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

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