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On strategic complementarity conditions in Bertrand oligopoly

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  • Rabah Amir
  • Isabel Grilo

Abstract

For Bertrand duopoly with linear costs, we establish via a single (counter-)example 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 to do so, 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. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Rabah Amir & Isabel Grilo, 2003. "On strategic complementarity conditions in Bertrand oligopoly," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 227-232, August.
    • Handle: RePEc:spr:joecth:v:22:y:2003:i:1:p:227-232
    DOI: 10.1007/s00199-002-0283-x
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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. KNAUFF, Malgorzata, 2006. "Market transparency and Bertrand competition," LIDAM Discussion Papers CORE 2006037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.

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    More about this item

    Keywords

    Keywords and Phrases: Price competition; Supermodularity; Single-crossing property; Critical sufficient condition.; JEL Classification Numbers: C72; D43; L13.;
    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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