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A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes

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Listed author(s):
  • Alexander Zimper

    ()

Abstract

This note demonstrates that a lattice game with strategic substitutes is dominancesolvable if and only if there exists a unique fixed point of the function that results from an iteration of the best response function. This finding complements a result of Milgrom and Roberts’ (1990) by which a lattice game with strategic complements is dominance-solvable if and only if there exists a unique Nash equilibrium. We illustrate our main result by an application to a model of Cournot outcomecompetition.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s00182-007-0073-6
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Article provided by Springer & Game Theory Society in its journal International Journal of Game Theory.

Volume (Year): 36 (2007)
Issue (Month): 1 (September)
Pages: 107-117

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Handle: RePEc:spr:jogath:v:36:y:2007:i:1:p:107-117
DOI: 10.1007/s00182-007-0073-6
Contact details of provider: Web page: http://www.springer.com

Web page: http://www.gametheorysociety.org/about.html

Order Information: Web: http://www.springer.com/economics/economic+theory/journal/182/PS2

Keywords: Supermodular games; Strategic substitutes; Iterative solution concepts; Unique Nash equilibrium; Cournot competition; C72; C62;

Other versions of this item:

Find related papers by JEL classification:
  • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
  • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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  1. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
  2. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  3. 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.
  4. Vives, Xavier, 2004. "Complementarities and Games: New Developments," CEPR Discussion Papers 4742, C.E.P.R. Discussion Papers.
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Cited by:

  1. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
  2. Harrison, Rodrigo & Jara-Moroni, Pedro, 2015. "A dominance solvable global game with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 1-11.
  3. Andrew J. Monaco & Tarun Sabarwal, 2016. "Games with strategic complements and substitutes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 65-91, June.
  4. Anne-Christine Barthel & Tarun Sabarwal, 2016. "Directional Monotone Comparative Statics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201601, University of Kansas, Department of Economics.
  5. Andrew Monaco & Tarun Sabarwal, 2012. "Monotone Comparative Statics in Games with both Strategic Complements and Strategic Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201236, University of Kansas, Department of Economics, revised Aug 2012.
  6. Andrew Monaco & Tarun Sabarwal, 2012. "Games with Strategic Heterogeneity," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201240, University of Kansas, Department of Economics, revised Nov 2012.
  7. repec:kan:wpaper:201502 is not listed on IDEAS
  8. repec:kan:wpaper:201412 is not listed on IDEAS

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