Price–Quantity Competition in a Duopoly Market With Price Similarities

Bertrand Crettez, Rabia Nessah and Raluca Parvulescu
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Bertrand Crettez: CRED - Centre de Recherche en Economie et Droit - Université Paris-Panthéon-Assas
Rabia Nessah: LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique
Raluca Parvulescu: LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique

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Abstract: We introduce a form of consumers' bounded rationality, price similarities , in a duopoly market with price–quantity competition. Price similarities occur when consumers do not react to slight differences in prices. In this case, firms' demands are determined by a sharing rule that depends on the quantities produced. Assuming a general form of the proportional sharing rule, we show that a pure strategy Nash equilibrium for the price–quantity game materializes if, and only if, price similarities are in place. We also show that there are two kinds of equilibrium. In the first kind, total supply equals total demand. By contrast, in the second kind, firms overproduce. Finally, we show how to compute the minimum level of the price similarities phenomenon necessary to ensure equilibrium existence given the market conditions.

Date: 2025-05-05
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Published in Journal of Economics and Management Strategy, 2025, ⟨10.1111/jems.12637⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05111469

DOI: 10.1111/jems.12637

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