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Farsighted stable sets in Hotelling’s location games

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  • Shino, Junnosuke
  • Kawasaki, Ryo

Abstract

We apply the farsighted stable set to two versions of Hotelling’s location games: one with a linear market and another with a circular market. It is shown that there always exists a farsighted stable set in both games, which consists of location profiles that yield equal payoff to all players. This stable set contains location profiles that reflect minimum differentiation as well as those profiles that reflect local monopoly. These results are in contrast to those obtained in the literature that use some variant of Nash equilibrium. While this stable set is unique when the number of players is two, uniqueness no longer holds for both models when the number of players is at least three.

Suggested Citation

  • Shino, Junnosuke & Kawasaki, Ryo, 2012. "Farsighted stable sets in Hotelling’s location games," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 23-30.
  • Handle: RePEc:eee:matsoc:v:63:y:2012:i:1:p:23-30
    DOI: 10.1016/j.mathsocsci.2011.09.001
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    References listed on IDEAS

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    Cited by:

    1. Nobuyuki Hanaki & Emily Tanimura & Nicolaas J. Vriend, 2016. "The Principle of Minimum Differentiation Revisited: Return of the Median Voter," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01317991, HAL.
    2. Ryo Kawasaki & Takashi Sato & Shigeo Muto, 2012. "Farsighted Stable Sets of Tariff Games," TERG Discussion Papers 281, Graduate School of Economics and Management, Tohoku University.
    3. Kawasaki, Ryo, 2015. "Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 8-12.
    4. Kawasaki, Ryo & Sato, Takashi & Muto, Shigeo, 2015. "Farsightedly stable tariffs," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 118-124.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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