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A Characterization of Strategic Complementarities

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Federico Echenique.

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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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Paper provided by University of California at Berkeley in its series Economics Working Papers with number E01-299.

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Date of creation: 01 Apr 2001
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Handle: RePEc:ucb:calbwp:e01-299

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  1. 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)
  2. 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)
  3. Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society. [Downloadable!]
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  4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  5. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March. [Downloadable!] (restricted)
  6. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
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  7. 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)
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  8. Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley. [Downloadable!]
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  9. Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, vol. 42(2), pages 307-314, February. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  11. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation, Yale University. [Downloadable!]
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  12. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
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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.)

  1. 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!]
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  2. 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!]
  3. 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!]
  4. 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!]
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