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'Strategic supplements' in games with polylinear interactions

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Author Info

  • 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.

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File URL: http://128.118.178.162/eps/game/papers/0411/0411008.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0411008.

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Length: 18 pages
Date of creation: 29 Nov 2004
Date of revision: 28 Feb 2005
Handle: RePEc:wpa:wuwpga:0411008

Note: Type of Document - pdf; pages: 18
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Web page: http://128.118.178.162

Related research

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

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References

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  1. 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 184-94, February.
  2. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  3. 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.
  4. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  5. M. Kandori & R. Rob, 2010. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Levine's Working Paper Archive 502, David K. Levine.
  6. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
  7. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  8. 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.
  9. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
  10. 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.
  11. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
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Cited by:
  1. Kukushkin, Nikolai S., 2012. "Cournot tatonnement and potentials," MPRA Paper 43188, University Library of Munich, Germany.
  2. Kukushkin, Nikolai S., 2013. "Approximate Nash equilibrium under the single crossing conditions," MPRA Paper 44320, University Library of Munich, Germany.
  3. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer, vol. 43(1), pages 45-66, April.

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