On pure-strategy Nash equilibria in price–quantity games

Iwan Bos and Dries Vermeulen

Journal of Mathematical Economics, 2021, vol. 96, issue C

Abstract: This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms simultaneously set prices and quantities. Existence of a pure-strategy equilibrium is proved for a class of price–quantity games. If the demand function is continuous, then the equilibrium outcome is similar to that of a price-only model. With discontinuous demand and limited spillover, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity thus yields Bertrand outcomes under a variety of market conditions.

Keywords: Bertrand oligopoly; Bertrand–Edgeworth competition; Cournot oligopoly; Oligopoly theory; Price–quantity competition (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:96:y:2021:i:c:s0304406821000392

DOI: 10.1016/j.jmateco.2021.102501

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