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Ordinal versus cardinal complementarity : the case of cournot oligopoly

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  • AMIR, Rabah

Abstract

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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Bibliographic Info

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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Keywords: Cournot oligopoly; complementarity; supermodularity; single-crossing property;

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References

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  1. Echenique, Federico, 2002. "A Characterization of Strategic Complementarities," Working Papers 1142, California Institute of Technology, Division of the Humanities and Social Sciences.
  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. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  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. AMIR, Rabah & LAMBSON, Val, 1999. "On the effects of entry in Cournot markets," CORE Discussion Papers 1999059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  7. 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.
  8. 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.
  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. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  11. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  12. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  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. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  15. 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.
  16. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
  17. 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).
  18. Hamilton, J.H. & Slutsky, S.M., 1988. "Endogenous Timing In Duopoly Games: Stackelberg Or Cournot Equilibria," Papers 88-4, Florida - College of Business Administration.
  19. 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).
  20. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
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Citations

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Cited by:
  1. Guy MEUNIER, 2011. "Emission permit trading between imperfectly competitive product markets," Working Papers 40770, Institut National de la Recherche Agronomique, France.
  2. Daria Onori, 2013. "Competition and Growth: Reinterpreting their Relationship," Working Papers halshs-00806994, HAL.
  3. Andrew F. Daughety, 2006. "Cournot Competition," Vanderbilt University Department of Economics Working Papers 0620, Vanderbilt University Department of Economics.
  4. Pavlo Prokopovych & Nicholas C.Yannelis, 2013. "On the Existence of Mixed Strategy Nash equilibria," Discussion Papers 50, Kyiv School of Economics.
  5. CALCIANO, Filippo L., 2011. "Oligopolistic competition with general complementarities," CORE Discussion Papers 2011054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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