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A Characterization of Strategic Complementarities

  • Echenique, Federico

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 California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1142.

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Date of creation: Oct 2002
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Publication status: Published: Published in Games and Economic Behavior 46 (2004) 325-347.
Handle: RePEc:clt:sswopa:1142
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  1. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  2. Echenique, Federico, 2002. "Finding All Equilibria," Working Papers 1153, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Econometric Society World Congress 2000 Contributed Papers 1906, Econometric Society.
  4. Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society.
  5. 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.
  6. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  7. 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).
  8. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  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. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  11. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation for Research in Economics, Yale University.
  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. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
  14. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  15. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  16. Federico Echenique, 2003. "The equilibrium set of two-player games with complementarities is a sublattice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 903-905, November.
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