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Hotelling competition with discrete consumers

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  • Byford, Martin C.

Abstract

Populating the Hotelling line with finitely many consumers produces a model of spatial competition that is challenging to analyse as it does not possess a Nash equilibrium in pure strategies. This paper characterises the mixed-strategy Nash equilibrium (MSNE) for the model. The MSNE is unique, symmetric, and its support converges to the equilibrium of the standard Hotelling model — with a continuum of consumers — from above. The results suggest that the standard model is a reasonable approximation of the MSNE for a market with a large number of discrete buyers. By contrast, the intensity of competition is significantly lower when the market is home to a small numbers of buyers. In this case the MSNE expected prices and profits are well above the equilibrium prices and profits of the standard model.

Suggested Citation

  • Byford, Martin C., 2025. "Hotelling competition with discrete consumers," Journal of Mathematical Economics, Elsevier, vol. 121(C).
    • Handle: RePEc:eee:mateco:v:121:y:2025:i:c:s0304406825001065
    DOI: 10.1016/j.jmateco.2025.103189
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    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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