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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. 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.
    3. 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.
    4. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    5. 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.
    6. 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, October.
    7. Barry Nalebuff, 2000. "Competing Against Bundles," Yale School of Management Working Papers ysm157, Yale School of Management.
    8. 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.
    Full references (including those not matched with items on IDEAS)

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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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