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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 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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 46 (2004)
Issue (Month): 2 (February)
Pages: 325-347

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Handle: RePEc:eee:gamebe:v:46:y:2004:i:2:p:325-347
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  1. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  2. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  3. Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," GE, Growth, Math methods 9912002, EconWPA.
  4. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  5. repec:elg:eebook:1585 is not listed on IDEAS
  6. Echenique, Federico & Edlin, Aaron S., 2002. "Mixed Equilibria in Games of Strategic Complements Are Unstable," Competition Policy Center, Working Paper Series qt2b85c93d, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley.
  7. 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.
  8. 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.
  9. Echenique, Federico, 2002. "Finding All Equilibria," Working Papers 1153, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  11. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  12. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  13. 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.
  14. 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.
  15. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  16. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation for Research in Economics, Yale University.
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