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Optimal strategies in n-person unilaterally competitive games

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  • DE WOLF, Olivier

    (Facultés Universitaires Saint-Louis (FUSL), B-1000, Brussels, Belgium and Center for Operations Research and Econometrics (CORE) at Université Catholique de Louvain (UCL), B-1348 Louvain-la-Neuve, Belgium)

Abstract

In this paper, we prove that the concept of value traditionally defined in the class of two-person zero-sum games can be adequately generalized to the class of n-person weakly unilaterally competitive games introduced by Kats & Thisse [KT92b]. We subsequently establish that if there exists an equilibrium in a game belonging to the latter class, then every player possesses at least an optimal strategy (i.e., a strategy yielding at least the value to this player). Furthermore, we show that, in all unilaterally competitive games that have a Nash equilibrium profile, a strategy profile is an equilibrium if and only if it is an optimal profile. From these results, we deduce a very strong foundation to the Nash equilibrium concept in unilaterally competitive games

Suggested Citation

  • DE WOLF, Olivier, 1999. "Optimal strategies in n-person unilaterally competitive games," LIDAM Discussion Papers CORE 1999049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1999049
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1999.html
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    References listed on IDEAS

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    1. DE WOLF, Olivier, 1998. "Fondements des concepts de solution en théorie des jeux," LIDAM Reprints CORE 1353, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. De Wolf, Olivier & Forges, Francoise, 1998. " Rational Choice in Strategic Environments: Further Observations," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(2), pages 529-535, June.
    3. repec:adr:anecst:y:1998:i:51:p:01 is not listed on IDEAS
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    Cited by:

    1. Stefanos Leonardos & Costis Melolidakis, 2018. "On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-28, September.
    2. Beaud, Jean-Pierre, 2017. "Antagonistic properties and n-person games," Center for Mathematical Economics Working Papers 327, Center for Mathematical Economics, Bielefeld University.
    3. Takuya Iimura, 2020. "Unilaterally competitive games with more than two players," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 681-697, September.
    4. Cédric Wanko, 2008. "Approche Conceptuelle et Algorithmique des Equilibres de Nash Robustes Incitatifs," Working Papers 08-03, LAMETA, Universtiy of Montpellier, revised Feb 2008.

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