Bertrand–Edgeworth oligopoly: Characterization of mixed strategy equilibria when some firms are large and the others are small

Salvadori, Neri; Francesco, Massimo A. De

doi:10.1111/meca.12382

Cited by 2 publications

(3 citation statements)

References 11 publications

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“…Basic properties of equilibria under the triopoly were discovered almost at the same time byHirata (2008) andDe Francesco andSalvadori (2008).…”

mentioning

confidence: 89%

“…A second direction of research focused on restricting the number of competing firms. Hirata (2009) and De Francesco and Salvadori (2010, 2015, 2016 have analyzed the triopoly price game with a decreasing and concave demand function, independently establishing a number of features of equilibria. 4 A third direction of research focused on a different demand function: inelastic market demand was adopted (Acemoglu, Bimpikis, andOzdaglar, 2009, andMark Armstrong andJohn Vickers, 2018).…”

Section: Introductionmentioning

confidence: 99%

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Bertrand‐Edgeworth game under oligopoly. General results and comparisons with duopoly

De Francesco,

Salvadori

2024

Metroeconomica

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This paper studies price competition among a given number of capacity‐constrained producers of a homogeneous commodity under the efficient rationing rule and constant (and identical) marginal cost until full capacity, when demand is a continuous, non‐increasing, and non‐negative function defined on the set of non‐negative prices and is positive, strictly decreasing, twice differentiable and (weakly) concave when positive. The focus is on general properties of equilibria in the region of the capacity space in which no pure strategy equilibria exist. We study how the properties that are known to hold for the duopoly are generalized to the oligopoly and we highlight the new properties that can arise in asymmetric oligopoly, which include the existence of an atom in the support of the equilibrium strategy of a firm smaller than the largest one, the properties that such an atom entails, the existence of gaps in the supports, and asymmetries in the equilibrium distributions of equally‐sized firms smaller than the largest one. Further, we provide results about the boundaries of the supports. Although the characterization of equilibria is far from being complete, this paper provides substantial elements in this direction.

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“…Basic properties of equilibria under the triopoly were discovered almost at the same time byHirata (2008) andDe Francesco andSalvadori (2008).…”

mentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Bertrand‐Edgeworth game under oligopoly. General results and comparisons with duopoly

De Francesco,

Salvadori

2024

Metroeconomica

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Bertrand-Edgeworth game under oligopoly. General results and comparisons with duopoly

De Francesco,

Salvadori

2023

Preprint

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This paper studies price competition among a given number of capacity-constrainedproducers of a homogeneous commodity under the efficient rationing rule andconstant (and identical) marginal cost until full capacity, whendemand is a continuous, non-increasing, and non-negative function defined onthe set of non-negative prices and is positive, strictly decreasing, twicedifferentiable and (weakly) concave when positive.The focus is on general properties of equilibria in the region of the capacityspace in which no pure strategy equilibria exist. We study how theproperties that are known to hold for the duopoly are generalized to theoligopoly and, on the contrary, what properties do not need to hold in oligopoly.Our inquiry reveals, among other properties, the possibility of an atom in the support of a firm smaller than the largest one and the properties that such an atom entails. Although the characterization of equilibria is far from being complete, this paper provides substantial elements in this direction. JEL: C72, D43, L13

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Bertrand–Edgeworth oligopoly: Characterization of mixed strategy equilibria when some firms are large and the others are small

Cited by 2 publications

References 11 publications

Bertrand‐Edgeworth game under oligopoly. General results and comparisons with duopoly

Bertrand‐Edgeworth game under oligopoly. General results and comparisons with duopoly

Bertrand-Edgeworth game under oligopoly. General results and comparisons with duopoly

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