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On strategic complementarity conditions in Bertrand oligopoly

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  • AMIR, Rabah
  • GRILO, Isabel

Abstract

For Bertrand duopoly with linear costs, we establish via a single counterexample that: (i) A new monotone transformation of the firms' profit functions may lead to the supermodularity of transformed profits when the standard log and identity transformations both fail, and (ii) Topkis's notion of critical sufficient condition for monotonicity of a Bertrand firm's best-reply correspondence cannot be extended to rely only on positive unit costs.

Suggested Citation

  • AMIR, Rabah & GRILO, Isabel, 2001. "On strategic complementarity conditions in Bertrand oligopoly," LIDAM Discussion Papers CORE 2001049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2001049
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2001.html
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    References listed on IDEAS

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    1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    2. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    Cited by:

    1. Olga Ivanova, 2004. "An influence of road pricing upon the performance of bus transit services in Oslo," ERSA conference papers ersa04p107, European Regional Science Association.
    2. Jan Zouhar & Martina Zouharova, 2020. "Stackelberg versus Cournot duopoly with asymmetric costs: primary markups, entry deterrence, and a comparison of social welfare and industry profits," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 89-96, April.
    3. Cumbul, Eray & Virág, Gábor, 2018. "Multilateral limit pricing in price-setting games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 250-273.
    4. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    5. KNAUFF, Malgorzata, 2006. "Market transparency and Bertrand competition," LIDAM Discussion Papers CORE 2006037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    More about this item

    Keywords

    Price competition; Supermodularity; Singlecrossing property; Critical sufficient condition;
    All these keywords.

    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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