Price and Quantity Competition in a Differentiated Duopoly

Singh, Nirvikar; Vives, Xavier

doi:10.2307/2555525

Cited by 2,340 publications

(1,737 citation statements)

References 13 publications

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“…3 Linear demand models have been used in the marketing and economics literatures previously to model differentiated duopolies (Shubik and Levitan, 1980, Singh and Vives, 1984, Raju el al., 1995, Jerath and Zhang, 2010. 4 The demand system above gives us a model of partial competition where β ∈ [0, 1) is the parameter that captures the degree of differentiation between the two e-tailers.…”

Section: Electronic Channelmentioning

confidence: 99%

Agency Selling or Reselling? Channel Structures in Electronic Retailing

2016

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In recent years, online retailers (e-tailers) have started allowing manufacturers direct access to their customers while charging a fee for providing this access, a format commonly referred to as agency selling. In this paper, we use a stylized theoretical model to answer a key question that e-tailers are facing: When should they use an agency selling format instead of using the more conventional reselling format? We find that agency selling is more efficient than reselling and leads to lower retail prices; however, the e-tailers end up giving control over retail prices to the manufacturer. Therefore, the reaction by the manufacturer, who makes electronic channel pricing decisions based on their impact on demand in the traditional channel (brick-and-mortar retailing), is an important factor for e-tailers to consider. We find that when sales in the electronic channel lead to a negative effect on demand in the traditional channel, e-tailers prefer agency selling, whereas when sales in the electronic channel lead to substantial stimulation of demand in the traditional channel, e-tailers prefer reselling. This preference is mediated by competition between e-tailers -as competition between them increases, e-tailers prefer to use agency selling. We also find that when e-tailers benefit from positive externalities from the sales of the focal product (such as additional profits from sales of associated products), retail prices may be lower under reselling than under agency selling, and the e-tailers prefer reselling under some conditions for which they would prefer agency selling without the positive externalities.

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Section: Electronic Channelmentioning

confidence: 99%

Agency Selling or Reselling? Channel Structures in Electronic Retailing

2016

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“…As shown by Singh and Vives (1984) this case is the dual of the traditional Bertrand oligopoly model, in which producers of substitute goods set prices. In this case, if a firm produces more than its competitor, the components produced in excess will not be sold (recall that only the bundle is valuable for consumers and there is no market for spare components).…”

Section: Quantity-setting Complementary Oligopolymentioning

confidence: 99%

Substituting Complements

Dari‐Mattiacci¹,

Parisi²

2006

Journal of Competition Law &Amp; Economics

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The presence of multiple sellers in the provision of (non-substitutable) complementary goods leads to outcomes that are worse than those generated by a monopoly (with a vertically integrated production of complements), a problem known in the economic literature as complementary oligopoly and recently popularized in the legal literature as the tragedy of the anticommons. We ask the following question: how many substitutes for each complement are necessary to render the presence of multiple sellers preferable to a monopoly? Highlighting the asymmetries between Cournot (quantity) and Bertrand (price) competition and their dual models, we show that the results crucially depend on whether firms compete by controlling price or quantity. Two substitutes per component are sufficient when firms choose price. However, when firms choose quantity, the availability of substitutes, regardless of their number, is ineffective. Considering more complex cases of multi-complementarity, we ask the related question of how many complements need to be substitutable and offer comments on equilibrium prices and quantities under different scenarios.JEL classification: D43, D62, K11, L13.

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“…In this paper we generalized Singh and Vives (1984) to account for asymmetry in the substitution e¤ects, and to study its implications for implicit collusion. The …rst result we found characterizes Cournot equilibrium: The symmetric benchmark …rm equilibrium prices, pro…ts and quantities are lower than those of the strong, and higher than those of the weak.…”

Section: Resultsmentioning

confidence: 99%

“…In this section we consider a Cournot duopoly which extends Singh and Vives (1984) allowing for asymmetry in the magnitude of the substitution e¤ects. This extension does not need any particular assumption, since market demands need not satisfy any symmetry conditions such as those required by the Slutsky equation (see e.g.…”

Section: A Linear Cournot Duopoly With Asymmetric Substitution E¤ectsmentioning

confidence: 99%

“…We extend Singh and Vives (1984) by allowing for asymmetry in the magnitude of the substitution e¤ects, deriving the equilibrium quantities, prices and profits. We compare them to those in a symmetric equivalent duopoly setting, namely a duopoly in which the substitution parameters are symmetric and equal to the average of the parameters in the asymmetric case.…”

Section: Introductionmentioning

confidence: 99%

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Partial Collusion with Asymmetric Cross-Price Effects

Savorelli

2010

SSRN Journal

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Asymmetries in cross-price elasticities have been demonstrated by several empirical studies. In this paper we study from a theoretical stance how introducing asymmetry in the substitution e¤ects in ‡uences the sustainability of collusion. We characterize the equilibrium of a linear Cournot duopoly with substitute goods, and consider substitution e¤ects which are asymmetric in magnitude. Within this framework, we study partial collusion using Friedman (1971) solution concept. Our main result shows that the interval of quantities supporting collusion in the asymmetric setting is always smaller than the interval in the symmetric benchmark. Thus, the asymmetry in the substitution e¤ects makes collusion more di¢ cult to sustain. This implies that previous Antitrust decisions could be reversed by considering the role of this kind of asymmetry.

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Price and Quantity Competition in a Differentiated Duopoly

Cited by 2,340 publications

References 13 publications

Agency Selling or Reselling? Channel Structures in Electronic Retailing

Agency Selling or Reselling? Channel Structures in Electronic Retailing

Substituting Complements

Partial Collusion with Asymmetric Cross-Price Effects

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