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'Strategic supplements' in games with polylinear interactions


  • Nikolai S Kukushkin

    (Dorodnicyn Computing Center of the Russian Academy of Sciences)


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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    References listed on IDEAS

    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.
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    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.
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    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.
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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. Kukushkin, Nikolai S., 2013. "Approximate Nash equilibrium under the single crossing conditions," MPRA Paper 44320, University Library of Munich, Germany.
    5. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    6. Yakov Babichenko, 2018. "Fast Convergence of Best-Reply Dynamics in Aggregative Games," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 333-346, February.
    7. Kukushkin, Nikolai S., 2016. "Nash equilibrium with discontinuous utility functions: Reny's approach extended," MPRA Paper 75862, University Library of Munich, Germany.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Kukushkin, Nikolai S., 2015. "Cournot tatonnement in aggregative games with monotone best responses," MPRA Paper 66976, University Library of Munich, Germany.

    More about this item


    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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