A unified model of horizontal differentiation with general spaces and irrational consumers

2025/06/27 by Labarthe, Aldric, Kerzreho, Yann
#Differential Geometry (math.DG) #FOS: Economics and business #FOS: Mathematics #General Finance (q-fin.GN) #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Theoretical Economics (econ.TH)

paper · doi:10.48550/arxiv.2507.01985

Abstract

We introduce a new microeconomic model of horizontal differentiation that unifies and extends previous developments inspired by the seminal work of Hotelling (1929). Our framework incorporates boundedly rational consumers, an unlimited number of firms, and arbitrary differentiation spaces with Riemannian manifolds. We argue that Riemannian geometry provides a natural and powerful tool for analyzing such models, offering fresh insights into firm behavior and market structure with complex products.

Citations

• Differentiation in a Two-Dimensional Market with Endogenous Sequential\n Entry
• Location Games on Networks: Existence and Efficiency of Equilibria
• The role of consumer networks in firms' multi-characteristics\n competition and market-share inequality
• Hotelling Games with Three, Four, and More Players*

Related

• Differentiation in a Two-Dimensional Market with Endogenous Sequential\n Entry
• Horizontal Product Differentiation in Varian's Model of Sales
• Notes on isotropic geometry of production models
• From Hotelling to Load Balancing: Approximation and the Principle of\n Minimum Differentiation
• Equilibrium selection: a geometric approach