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A Characterization of Strategic Complementarities

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  • Federico Echenique

    (Universidad de la Republica, Uruguay; & Universidad Torcuato Di Tella, Argentina)

Abstract

I characterize games for which there is an order on strategies such that the game has strategic complementarities. I prove that, with some qualifications, games with a unique equilibrium have complementarities if and only if Cournot best-response dynamics has no cycles; and that all games with multiple equilibria have complementarities. This is a negative result because it implies that the predictive power of complementarities alone is very weak. As an application of my results I show that generic 2 X 2 games either have no pure-strategy equilibria, or are GSC.

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File URL: http://128.118.178.162/eps/ge/papers/0103/0103001.pdf
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Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 0103001.

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Length: 19 pages
Date of creation: 23 Apr 2001
Date of revision:
Handle: RePEc:wpa:wuwpge:0103001

Note: 19 pages, Acrobat .pdf
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Web page: http://128.118.178.162

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  1. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  2. Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley.
  3. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  6. Echenique, Federico & Edlin, Aaron S., 2002. "Mixed Equilibria in Games of Strategic Complements Are Unstable," Department of Economics, Working Paper Series qt26r9r912, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  7. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation for Research in Economics, Yale University.
  8. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  9. 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.
  10. 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.
  11. 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).
  12. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  13. Federico Echenique, 2002. "Finding All Equilibria," Levine's Working Paper Archive 506439000000000059, David K. Levine.
  14. Federico Echenique, 2003. "The equilibrium set of two-player games with complementarities is a sublattice," Economic Theory, Springer, vol. 22(4), pages 903-905, November.
  15. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
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Cited by:
  1. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, Southern Economic Association, vol. 71(3), pages 636-660, January.
  2. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
  3. Takahashi, Satoru, 2008. "The number of pure Nash equilibria in a random game with nondecreasing best responses," Games and Economic Behavior, Elsevier, vol. 63(1), pages 328-340, May.
  4. Amir, Rabah, 2005. "Ordinal versus cardinal complementarity: The case of Cournot oligopoly," Games and Economic Behavior, Elsevier, vol. 53(1), pages 1-14, October.
  5. Tang, Pingzhong & Lin, Fangzhen, 2011. "Two equivalence results for two-person strict games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 479-486, March.
  6. 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).
  7. 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).
  8. Jeremy Fox & Natalia Lazzati, 2013. "Identification of discrete choice models for bundles and binary games," CeMMAP working papers CWP04/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Berger, Ulrich, 2009. "The convergence of fictitious play in games with strategic complementarities: A Comment," MPRA Paper 20241, University Library of Munich, Germany.

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