A characterization of strategic complementarities

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A characterization of strategic complementarities

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Federico Echenique

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Federico Echenique

Abstract

I characterize games for which there is an order on strategies such that the game has strategic complementarities. I prove that, with some quali cations, games with a unique equilibrium have complementarities if and only if Cournot best-response dynamics has no cycles; and that all games with multiple equi- libria have complementarities. As applications of my results, I show: 1. That generic 2X2 games either have no pure-strategy equilibria, or have complementarities. 2. That generic two-player nite ordinal potential games have complementarities.

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Paper provided by Department of Economics - dECON in its series Documentos de Trabajo (working papers) with number 0501.

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Length: 25 pages
Date of creation: Dec 2001
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Handle: RePEc:ude:wpaper:0501

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Article
- Echenique, Federico, 2004. "A characterization of strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 325-347, February. [Downloadable!] (restricted)
Paper
- Echenique, Federico, 2002. "A Characterization of Strategic Complementarities," Working Papers 1142, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
- Federico Echenique., 2001. "A Characterization of Strategic Complementarities," Economics Working Papers E01-299, University of California at Berkeley. [Downloadable!]
- Federico Echenique, 2001. "A Characterization of Strategic Complementarities," Department of Economics, Working Paper Series 1020, Department of Economics, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
- Federico Echenique, 2001. "A Characterization of Strategic Complementarities," GE, Growth, Math methods 0103001, EconWPA. [Downloadable!]

Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November. [Downloadable!] (restricted)
Rabah Amir & Val E. Lambson, 1998. "On the Effects of Entry in Cournot Markets," CIE Discussion Papers 1998-06, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
Other versions:
- AMIR, Rabah & LAMBSON, Val, 1999. "On the effects of entry in Cournot markets," CORE Discussion Papers 1999059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
- Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society. [Downloadable!]
- Amir, Rabah & Lambson, Val E, 2000. "On the Effects of Entry in Cournot Markets," Review of Economic Studies, Blackwell Publishing, vol. 67(2), pages 235-54, April.
Lippman, Steven A. & Mamer, John W. & McCardle, Kevin F., 1987. "Comparative statics in non-cooperative games via transfinitely iterated play," Journal of Economic Theory, Elsevier, vol. 41(2), pages 288-303, April. [Downloadable!] (restricted)
Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation, Yale University. [Downloadable!]
Other versions:
- Stephen Morris & Hyun S Shin, 2001. "Global Games: Theory and Applications," Levine's Working Paper Archive 122247000000001080, David K. Levine. [Downloadable!]
- Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275R, Cowles Foundation, Yale University, revised Aug 2001. [Downloadable!]
Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September. [Downloadable!] (restricted)
Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
Other versions:
- Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March. [Downloadable!] (restricted)
Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
Other versions:
- 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).
Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August. [Downloadable!] (restricted)
Other versions:
- Rabah, Amir, . "Cournot Oligopoly and the Theory of Supermodular Games," IVS discussion paper series 489, Institut für Volkswirtschaft und Statistik (IVS), University of Mannheim.
Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley. [Downloadable!]
Other versions:
- Federico Echenique, 1999. "Comparative Statics by Adaptative Dynamics and the Correspondence Principle," Documentos de Trabajo (working papers) 2099, Department of Economics - dECON. [Downloadable!]
- Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," GE, Growth, Math methods 9912002, EconWPA. [Downloadable!]
- Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Econometric Society World Congress 2000 Contributed Papers 1906, Econometric Society. [Downloadable!]
- Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March. [Downloadable!] (restricted)
Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, vol. 42(2), pages 307-314, February. [Downloadable!] (restricted)
Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Rabah Amir & Filomena Garcia & Malgorzata Knauff, 2006. "Endogenous Heterogeneity in Strategic Models: Symmetry-breaking via Strategic Substitutes and Nonconcavities," Working Papers 2006/29, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon.. [Downloadable!]
Other versions:
- AMIR, Rabah & GARCIA, Filomena & KNAUFF, Malgorzata, 2006. "Endogenous heterogeneity in strategic models: symmetry-breaking via strategic substitutes and nonconcavities," CORE Discussion Papers 2006008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
AMIR, Rabah, 2004. "Ordinal versus cardinal complementarity : the case of cournot oligopoly," CORE Discussion Papers 2004036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Other versions:
- Amir, Rabah, 2005. "Ordinal versus cardinal complementarity: The case of Cournot oligopoly," Games and Economic Behavior, Elsevier, vol. 53(1), pages 1-14, October. [Downloadable!] (restricted)
AMIR, Rabah, 2003. "Supermodularity and complementarity in ecnomics: an elementary survey," CORE Discussion Papers 2003104, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Other versions:
- Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, Southern Economic Association, vol. 71(3), pages 636-660, January.
TESORIERE, Antonio, 2005. "Endogenous R&D symmetry in linear duopoly with one-way spillovers," CORE Discussion Papers 2005045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Mathevet, Laurent, 2007. "Supermodular Bayesian implementation: Learning and incentive design," Working Papers 1265, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]

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