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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
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Handle: RePEc:cor:louvco:2004036
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  1. Hamilton, J.H. & Slutsky, S.M., 1988. "Endogenous Timing In Duopoly Games: Stackelberg Or Cournot Equilibria," Papers 88-4, Florida - College of Business Administration.
  2. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  3. 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).
  4. Amir, R., 1991. "Sensitivity analysis of multi-sector optimal economic dynamics," CORE Discussion Papers 1991006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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.
  6. Echenique, Federico, 2001. "A Characterization of Strategic Complementarities," Department of Economics, Working Paper Series qt5w13s4z2, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  8. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  10. 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.
  11. 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).
  12. 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.
  13. Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, May.
  14. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  15. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
  16. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  17. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  18. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  19. 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.
  20. Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
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