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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

    as
    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.
    3. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    4. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
    5. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    6. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
    7. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    8. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    9. Smith, Tony E, 1974. "On the Existence of Most-Preferred Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 184-194, February.
    10. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    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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    Citations

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    Cited by:

    1. Kukushkin, Nikolai S., 2016. "Nash equilibrium with discontinuous utility functions: Reny's approach extended," MPRA Paper 75862, University Library of Munich, Germany.
    2. Kukushkin, Nikolai S., 2015. "Cournot tatonnement and potentials," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 117-127.
    3. Kukushkin, Nikolai S., 2018. "A universal construction generating potential games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 331-340.
    4. Richard Klima & Daan Bloembergen & Rahul Savani & Karl Tuyls & Daniel Hennes & Dario Izzo, 2016. "Space Debris Removal: A Game Theoretic Analysis," Games, MDPI, Open Access Journal, vol. 7(3), pages 1-18, August.
    5. Kukushkin, Nikolai S., 2013. "Approximate Nash equilibrium under the single crossing conditions," MPRA Paper 44320, University Library of Munich, Germany.
    6. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    7. Federico Quartieri & Pier Luigi Sacco, 2016. "A note on the symmetry of all Nash equilibria in games with increasing best replies," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 81-93, April.
    8. Kukushkin, Nikolai S., 2015. "Cournot tatonnement in aggregative games with monotone best responses," MPRA Paper 66976, University Library of Munich, Germany.
    9. 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.

    More about this item

    Keywords

    Strategic complements; Strategic substitutes; Best response dynamics; Potential games;

    JEL classification:

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

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