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Hotelling's Main Street Model: Undercut-Proof Equilibrium as a Constrained Optimization Problem

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  • Stephen Martin

Abstract

The paper analyzes a two-stage Main Street model. In the second stage, taking locations as given, each of two firms sets price to maximize own profit, subject to the constraint that it is not profitable for the other firm to undercut its price at its location. We find constrained price best-response equations and pure-strategy equilibrium prices for all pairs of locations. In the first stage, firms noncooperatively pick locations to maximize second-stage payoffs. We find location best-response equations and equilibrium locations. Equilibrium locations are efficient in the sense of minimizing transportation cost.

Suggested Citation

  • Stephen Martin, 2025. "Hotelling's Main Street Model: Undercut-Proof Equilibrium as a Constrained Optimization Problem," Purdue University Economics Working Papers 1354, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1354
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    File URL: https://business.purdue.edu/research/working-papers-series/2025/1354.pdf
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    References listed on IDEAS

    as
    1. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-922, July.
    2. Iskakov, Mikhail & Iskakov, Alexey, 2012. "Solution of the Hotelling’s game in secure strategies," Economics Letters, Elsevier, vol. 117(1), pages 115-118.
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    More about this item

    Keywords

    Main Street; Hotelling; price undercutting;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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