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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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2004036.

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Date of creation: 00 Jun 2004
Date of revision:
Handle: RePEc:cor:louvco:2004036
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  1. 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.
  2. AMIR, Rabah, 1994. "Cournot Oligopoly and the Theory of Supermodular Games," CORE Discussion Papers 1994013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  4. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  5. Federico Echenique, 2001. "A characterization of strategic complementarities," Documentos de Trabajo (working papers) 0501, Department of Economics - dECON.
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  7. 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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  9. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  10. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
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  14. ROBERTS, John, . "On the existence of Cournot equilibrium without concave profit functions," CORE Discussion Papers RP 260, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. 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 861-89, July.
  16. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  17. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  18. 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.
  19. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  20. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
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