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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. 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).
  2. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  3. Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society.
  4. Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley.
  5. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  6. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation for Research in Economics, Yale University.
  7. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  8. 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.
  9. 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.
  10. 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.
  11. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  12. 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.
  13. Federico Echenique, 2002. "Finding All Equilibria," Levine's Working Paper Archive 506439000000000059, David K. Levine.
  14. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  15. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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Citations

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Cited by:
  1. Roy, Sunanda & Sabarwal, Tarun, 2010. "Characterizing Stability Properties in Games with Strategic Substitutes," Staff General Research Papers 32009, Iowa State University, Department of Economics.
  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. Amir, Rabah, 2005. "Ordinal versus cardinal complementarity: The case of Cournot oligopoly," Games and Economic Behavior, Elsevier, vol. 53(1), pages 1-14, October.
  4. 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.
  5. Berger, Ulrich, 2009. "The convergence of fictitious play in games with strategic complementarities: A Comment," MPRA Paper 20241, University Library of Munich, Germany.
  6. 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.
  7. AMIR, Rabah, 2003. "Supermodularity and complementarity in economics: an elementary survey," CORE Discussion Papers 2003104, 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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