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'Strategic supplements' in games with polylinear interactions

Author

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  • Nikolai S Kukushkin

    (Dorodnicyn Computing Center of the Russian Academy of Sciences)

Abstract

Strategic games are considered where: every player chooses from a compact subset of the real line; the partners' choices affect each player's utility only through their scalar aggregate, which is affine in every single partner's choice; if the choices of all players but two are fixed, then both functions expressing the dependence of one player's aggregate on the other's choice have the same slope; the best response correspondence of each player is nonempty-valued and increases in the aggregate. Every such game admits a 'Cournot potential,' i.e., Nash equilibria exist and all best response improvement paths, in a sense, lead to them.

Suggested Citation

  • 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.
    • Handle: RePEc:wpa:wuwpga:0411008
    Note: Type of Document - pdf; pages: 18
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0411/0411008.pdf
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    References listed on IDEAS

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    1. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
    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.
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    9. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
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    Citations

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    Cited by:

    1. Kukushkin, Nikolai S., 2018. "A universal construction generating potential games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 331-340.
    2. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 45-66, April.
    3. Kukushkin, Nikolai S., 2015. "Cournot tatonnement and potentials," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 117-127.
    4. Péter Bayer & György Kozics & Nóra Gabriella Szőke, 2020. "Best-Response Dynamics in Directed Network Games," CEU Working Papers 2020_1, Department of Economics, Central European University.
    5. Nikolai S. Kukushkin, 2016. "Cournot Tatonnement in Aggregative Games with Monotone Best Responses," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 31-45, Springer.
    6. Federico Quartieri & Ryusuke Shinohara, 2015. "Coalition-proofness in a class of games with strategic substitutes," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 785-813, November.
    7. Nikolai Kukushkin, 2015. "The single crossing conditions for incomplete preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 225-251, February.
    8. Kukushkin, Nikolai S., 2022. "Ordinal status games on networks," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    9. Kukushkin, Nikolai S., 2013. "Approximate Nash equilibrium under the single crossing conditions," MPRA Paper 44320, University Library of Munich, Germany.
    10. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    11. Yakov Babichenko, 2018. "Fast Convergence of Best-Reply Dynamics in Aggregative Games," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 333-346, February.
    12. Kukushkin, Nikolai S., 2016. "Nash equilibrium with discontinuous utility functions: Reny's approach extended," MPRA Paper 75862, University Library of Munich, Germany.
    13. Richard Klima & Daan Bloembergen & Rahul Savani & Karl Tuyls & Daniel Hennes & Dario Izzo, 2016. "Space Debris Removal: A Game Theoretic Analysis," Games, MDPI, vol. 7(3), pages 1-18, August.
    14. P'eter Bayer & Gyorgy Kozics & N'ora Gabriella SzH{o}ke, 2021. "Best-response dynamics in directed network games," Papers 2101.03863, arXiv.org.

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    More about this item

    Keywords

    Strategic complements; Strategic substitutes; Best response dynamics; Potential games;
    All these keywords.

    JEL classification:

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

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