Cournot Competition on the Hotelling Line Yields at Most Three Varieties

• Published in: Review of industrial organization Vol. 65; no. 3; pp. 669 - 704
• Main Authors: Cosnita-Langlais, Andreea, Langlais, Eric
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2024; Springer Nature B.V
• Subjects: Accidents; Clustering; Competition; Consumers; Costs; Differentiation; Duopoly; Economics; Economics and Finance; Equilibrium; Industrial Organization; Markets; Microeconomics; Oligopoly; Product differentiation; Products liability; Quantitative Finance; Sales territories; Uniqueness; Cournot competition; D43; D47; Product choice; K13; Strategic location; K23; L25; L13; Horizontal differentiation; Spatial model; Product liability; Oligopoly; product choice; strategic location; product liability; horizontal differentiation; spatial model; oligopoly
• ISSN: 0889-938X; 1573-7160
• DOI: 10.1007/s11151-024-09979-5

This paper reexamines the equilibrium product choices in a spatial Cournot n - oligopoly on the linear market by considering the case of output that accidentally harms consumers and firms that are subject to product liability. We characterize the resulting spatial pattern in terms of uniqueness and stability. For low levels of the unit cost of accident, central agglomeration is the unique and stable location equilibrium. For a high enough unit cost of accident, multiple equilibria exist: from central agglomeration to partial dispersion (both asymmetric and symmetric). In this case we show that asymmetric dispersion equilibria as well as symmetrical three-variety equilibria are unstable, whereas there always exists a symmetrical two-variety location equilibrium that is stable. Finally, complete dispersion appears as a very specific case that is limited to duopoly and triopoly: For markets with more firms, equilibrium product differentiation involves partial clustering on three varieties/locations.