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Utilitarian Preferences and Potential Games

Author

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  • Hannu Salonen

    (Department of Economics, University of Turku, Finland)

Abstract

We study games with utilitarian preferences: the sum of individual utility functions is a generalized ordinal potential for the game. It turns out that generically, any finite game with a potential, ordinal potential, or generalized ordinal potential is better reply equivalent to a game with utilitarian preferences. It follows that generically, finite games with a generalized ordinal potential are better reply equivalent to potential games. For infinite games we show that a continuous game has a continuous ordinal potential, iff there is a better reply equivalent continuous game with utilitarian preferences. For such games we show that best reply improvement paths can be used to approximate equilibria arbitrarily closely.

Suggested Citation

  • Hannu Salonen, 2013. "Utilitarian Preferences and Potential Games," Discussion Papers 85, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp85
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    File URL: http://www.ace-economics.fi/kuvat/dp85.pdf
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    References listed on IDEAS

    as
    1. Voorneveld, Mark & Norde, Henk, 1997. "A Characterization of Ordinal Potential Games," Games and Economic Behavior, Elsevier, vol. 19(2), pages 235-242, May.
    2. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    3. Voorneveld, M. & Norde, H.W., 1996. "A Characterization of Ordinal Potential Games," Other publications TiSEM a48550d5-29e7-48ec-b9d4-5, Tilburg University, School of Economics and Management.
    4. Salonen, Hannu & Vartiainen, Hannu, 2010. "On the existence of undominated elements of acyclic relations," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 217-221, November.
    5. Giovanni Facchini & Freek van Megen & Peter Borm & Stef Tijs, 1997. "Congestion Models And Weighted Bayesian Potential Games," Theory and Decision, Springer, vol. 42(2), pages 193-206, March.
    6. Voorneveld, Mark, 1997. "Equilibria and approximate equilibria in infinite potential games," Economics Letters, Elsevier, vol. 56(2), pages 163-169, October.
    7. Friedman, James W. & Mezzetti, Claudio, 2001. "Learning in Games by Random Sampling," Journal of Economic Theory, Elsevier, vol. 98(1), pages 55-84, May.
    8. 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.
    9. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    potential games; best reply equivalence; utilitarian preferences;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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