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Ordinal versus cardinal complementarity: The case of Cournot oligopoly

  • Amir, Rabah

While ordinal complementarity is more general than cardinal complementarity, the corresponding global sufficient conditions placed on the primitives of a constrained optimization problem are generally not comparable. We explore this issue in detail for the special case of a Cournot firm. We derive necessary and sufficient conditions for downward-sloping best-responses by imposing the ordinal test only for output levels that are actually reached. Both global tests, cardinal and ordinal, are shown not to be critical sufficient conditions. Finally, we confirm that checking supermodularity of suitably transformed profits can work when the global tests for ordinal and cardinal complementarity both fail.

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

Volume (Year): 53 (2005)
Issue (Month): 1 (October)
Pages: 1-14

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Handle: RePEc:eee:gamebe:v:53:y:2005:i:1:p:1-14
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Federico Echenique, 2001. "A Characterization of Strategic Complementarities," GE, Growth, Math methods 0103001, EconWPA.
  2. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  3. Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society.
  4. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
  5. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
  6. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  7. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x.
  8. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
  9. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  10. Roberts, John & Sonnenschein, Hugo, 1976. "On the existence of Cournot equilbrium without concave profit functions," Journal of Economic Theory, Elsevier, vol. 13(1), pages 112-117, August.
  11. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  12. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  13. Amir, Rabah & Jin, Jim Y., 2001. "Cournot and Bertrand equilibria compared: substitutability, complementarity and concavity," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 303-317, March.
  14. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
  15. 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).
  16. Bulow, Jeremy & Geanakoplos, John & Klemperer, Paul, 1985. "Holding Idle Capacity to Deter Entry [The Role of Investment in Entry Deterrence]," Economic Journal, Royal Economic Society, vol. 95(377), pages 178-82, March.
  17. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
  18. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
  19. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
  20. Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, May.
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