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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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Suggested Citation

  • Amir, Rabah, 2005. "Ordinal versus cardinal complementarity: The case of Cournot oligopoly," Games and Economic Behavior, Elsevier, vol. 53(1), pages 1-14, October.
  • Handle: RePEc:eee:gamebe:v:53:y:2005:i:1:p:1-14
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    Cited by:

    1. Daria Onori, 2015. "Competition and Growth: Reinterpreting their Relationship," Manchester School, University of Manchester, vol. 83(4), pages 398-422, July.
    2. Bertrand Koebel & François Laisney, 2016. "Aggregation with Cournot Competition: An Empirical Investigation," Annals of Economics and Statistics, GENES, issue 121-122, pages 91-119.
    3. Ewerhart, Christian, 2014. "Cournot games with biconcave demand," Games and Economic Behavior, Elsevier, vol. 85(C), pages 37-47.
    4. Guy Meunier, 2011. "Emission Permit Trading Between Imperfectly Competitive Product Markets," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 50(3), pages 347-364, November.
    5. Prokopovych, Pavlo & Yannelis, Nicholas C., 2014. "On the existence of mixed strategy Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 87-97.
    6. Andrew F. Daughety, 2006. "Cournot Competition," Vanderbilt University Department of Economics Working Papers 0620, Vanderbilt University Department of Economics.
    7. CALCIANO, Filippo L., 2011. "Oligopolistic competition with general complementarities," CORE Discussion Papers 2011054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Tesoriere, Antonio, 2017. "Stackelberg equilibrium with many leaders and followers. The case of zero fixed costs," Research in Economics, Elsevier, vol. 71(1), pages 102-117.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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