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Best-response potential for Hotelling pure location games

Author

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  • Iimura, Takuya
  • von Mouche, Pierre
  • Watanabe, Takahiro

Abstract

We revisit two-person one-dimensional pure location games à la Anderson et al. (1992) and show that they admit continuous best-response potential functions (Voorneveld, 2000) if demand is sufficiently elastic (to the extent that the Principle of Minimum Differentiation fails); if demand is not that elastic (or is completely inelastic) they still admit continuous quasi-potential functions (Schipper, 2004). We also show that, even if a continuous best-response potential function exists, a generalized ordinal potential function (Monderer and Shapley, 1996) need not exist.

Suggested Citation

  • Iimura, Takuya & von Mouche, Pierre & Watanabe, Takahiro, 2017. "Best-response potential for Hotelling pure location games," Economics Letters, Elsevier, vol. 160(C), pages 73-77.
    • Handle: RePEc:eee:ecolet:v:160:y:2017:i:c:p:73-77
    DOI: 10.1016/j.econlet.2017.08.025
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    References listed on IDEAS

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    1. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
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    3. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    4. A. Smithies, 1941. "Optimum Location in Spatial Competition," Journal of Political Economy, University of Chicago Press, vol. 49(3), pages 423-423.
    5. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Symmetric games; Location games; Best-response potential games; Pure Nash equilibrium existence;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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