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Better response dynamics and Nash equilibrium in discontinuous games

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  • Kukushkin, Nikolai S.

Abstract

Philip Reny’s approach to games with discontinuous utility functions can work outside its original context. The existence of Nash equilibrium and the possibility to approach the equilibrium set with a finite number of individual improvements are established, under conditions weaker than the better reply security, for three classes of strategic games: potential games, games with strategic complements, and aggregative games with appropriate monotonicity conditions.

Suggested Citation

  • Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    • Handle: RePEc:eee:mateco:v:74:y:2018:i:c:p:68-78
    DOI: 10.1016/j.jmateco.2017.11.005
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    Citations

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    Cited by:

    1. Ben Amiet & Andrea Collevecchio & Kais Hamza, 2020. "When "Better" is better than "Best"," Papers 2011.00239, arXiv.org.
    2. Kukushkin, Nikolai S., 2020. "Ordinal status games on networks," MPRA Paper 104729, University Library of Munich, Germany.
    3. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    4. Kukushkin, Nikolai S., 2019. "Equilibria in ordinal status games," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 130-135.
    5. Nikolai S. Kukushkin & Pierre von Mouche, 2018. "Cournot tatonnement and Nash equilibrium in binary status games," Economics Bulletin, AccessEcon, vol. 38(2), pages 1038-1044.

    More about this item

    Keywords

    Discontinuous game; Potential game; Bertrand competition; Strategic complements; Aggregative game;

    JEL classification:

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

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