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The dual of Bertrand with homogeneous products is Cournot with perfect complements

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  • Paolo Bertoletti

Abstract

The quantity-setting (Cournot) oligopoly with perfect complements is dual to the price-setting (Bertrand) oligopoly with homogeneous goods. Under mild technical conditions, the former setting has a unique (pure strategy) Nash equilibrium with null quantities.

Suggested Citation

  • Paolo Bertoletti, 2022. "The dual of Bertrand with homogeneous products is Cournot with perfect complements," Working Papers 490, University of Milano-Bicocca, Department of Economics.
    • Handle: RePEc:mib:wpaper:490
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    References listed on IDEAS

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    1. Michael Spence, 1976. "Product Selection, Fixed Costs, and Monopolistic Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(2), pages 217-235.
    2. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    3. Hugo Sonnenschein, 1968. "The Dual of Duopoly Is Complementary Monopoly: or, Two of Cournot's Theories Are One," Journal of Political Economy, University of Chicago Press, vol. 76(2), pages 316-316.
    4. Claude d’Aspremont & Rodolphe Dos Santos Ferreira, 2021. "The Economics of Competition, Collusion and In-between," Springer Books, Springer, number 978-3-030-63602-9, December.
    5. Amir, Rabah & Evstigneev, Igor V., 2018. "A new look at the classical Bertrand duopoly," Games and Economic Behavior, Elsevier, vol. 109(C), pages 99-103.
    6. Eilon Solan & Nicolas Vieille, 2006. "Equilibrium uniqueness with perfect complements," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 721-726, August.
    7. Barry Nalebuff, 2000. "Competing Against Bundles," Yale School of Management Working Papers ysm157, Yale School of Management.
    8. Samuelson, Paul A, 1974. "Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1255-1289, December.
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    More about this item

    Keywords

    Cournot duopoly; Bertrand duopoly; perfect complements; homogeneous products.;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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