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A characterization of strategic complementarities

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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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File URL: http://decon.edu.uy/publica/2001/Doc0501.pdf
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Bibliographic Info

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
Date of revision:
Handle: RePEc:ude:wpaper:0501

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Related research

Keywords: Strategic complementarities; supermodular games; non-standard analysis; Cournot best-response dynamics; potential games.;

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References

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  1. Federico Echenique & Aaron Edlin, 2001. "Mixed Equilibria in Games of Strategic Complements are Unstable," Levine's Working Paper Archive 563824000000000161, David K. Levine.
  2. Amir, Rabah & Lambson, Val E, 2000. "On the Effects of Entry in Cournot Markets," Review of Economic Studies, Wiley Blackwell, vol. 67(2), pages 235-54, April.
  3. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  4. 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.
  5. Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," GE, Growth, Math methods 9912002, EconWPA.
  6. 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.
  7. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  8. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  9. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation for Research in Economics, Yale University.
  10. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  11. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  12. 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.
  13. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  14. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  15. Federico Echenique, 2002. "Finding All Equilibria," Levine's Working Paper Archive 506439000000000059, David K. Levine.
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Citations

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Cited by:
  1. 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.
  2. 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).
  3. 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.
  4. Berger, Ulrich, 2009. "The convergence of fictitious play in games with strategic complementarities: A Comment," MPRA Paper 20241, University Library of Munich, Germany.
  5. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing Stability Properties in Games with Strategic Substitutes," Staff General Research Papers 34778, Iowa State University, Department of Economics.
  6. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, Southern Economic Association, vol. 71(3), pages 636-660, January.
  7. 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).
  8. 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).
  9. 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.

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