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On the Existence and Social Optimality of Equilibria in a Hotelling Game with Uncertain Demand and Linear-Quadratic Costs

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  • Krol Michal

    () (The University of Manchester)

Abstract

This paper examines a variant of the Hotelling two-stage mill-pricing duopoly game with “linear-quadratic” transport costs and the uniform customer distribution subject to a random shock. The demand is equally likely to be found anywhere in a fixed interval of feasible product characteristics, with the ex-post differentiation of tastes parametrized to reflect the degree of uncertainty. It turns out that, for uncertainty big enough, the presence of a linear component in the cost function no longer rules out an analytical solution to the game, which is a common problem in spatial competition models. In particular, a subgame-perfect equilibrium is shown to exist in which the firms’ locations approach the socially efficient ones as uncertainty further increases, regardless of the curvature of the cost function. When the demand uncertainty reaches maximum, mill-pricing is equivalent to spatial price discrimination under the most general conditions.

Suggested Citation

  • Krol Michal, 2011. "On the Existence and Social Optimality of Equilibria in a Hotelling Game with Uncertain Demand and Linear-Quadratic Costs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-22, March.
  • Handle: RePEc:bpj:bejtec:v:11:y:2011:i:1:n:7
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    References listed on IDEAS

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    1. Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-640, May.
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    17. Mérel Pierre R & Sexton Richard J., 2010. "Kinked-Demand Equilibria and Weak Duopoly in the Hotelling Model of Horizontal Differentiation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-34, April.
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    Cited by:

    1. Król, Michał, 2012. "Product differentiation decisions under ambiguous consumer demand and pessimistic expectations," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 593-604.
    2. Arcan Nalca, & Tamer Boyaci, & Saibal Ray, 2017. "Brand positioning and consumer taste information," ESMT Research Working Papers ESMT-17-01_R1, ESMT European School of Management and Technology, revised 04 Dec 2017.
    3. Arcan Nalca, & Tamer Boyaci, & Saibal Ray, 2017. "Consumer taste uncertainty in the context of store brand and national brand competition," ESMT Research Working Papers ESMT-17-01, ESMT European School of Management and Technology.
    4. repec:eee:ejores:v:268:y:2018:i:2:p:555-568 is not listed on IDEAS

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • R32 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location - - - Other Spatial Production and Pricing Analysis

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