IDEAS home Printed from https://ideas.repec.org/p/rut/rutres/200808.html
   My bibliography  Save this paper

Farsighted Stable Sets in Hotelling's Location Games

Author

Listed:
  • Junnosuke Shino

    (Rutgers University)

Abstract

We apply farsighted stable set to two versions of Hotelling's location games: one with linear market and another with circular market. It is shown that there always exists a farsighted stable set in both games. In particular, the set of all location profiles that yields equal payoff across all players is shown to be a farsighted stable set. 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 by equilibrium analysis. While the stable set uniquely exists when the number of players is 2, the uniqueness is not guaranteed when n>2. In particular, we exhibit multiple stable sets in three person location games. We provide possible interpretations of these farsighted stable sets from the viewpoint of players' bargaining power and coalition.

Suggested Citation

  • Junnosuke Shino, 2008. "Farsighted Stable Sets in Hotelling's Location Games," Departmental Working Papers 200808, Rutgers University, Department of Economics.
    • Handle: RePEc:rut:rutres:200808
    as

    Download full text from publisher

    File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2008-08.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 27-49.
    2. Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2008. "Farsighted coalitional stability in TU-games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 303-313, November.
    3. Noritsugu Nakanishi, 2009. "Noncooperative farsighted stable set in an n-player prisoners’ dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 249-261, June.
    4. Masahisa Fujita & Jacques-François Thisse, 1986. "Spatial Competition with a Land Market: Hotelling and Von Thunen Unified," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 819-841.
    5. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    6. Akihiro Suzuki & Shigeo Muto, 2005. "Farsighted Stability in an n-Person Prisoner’s Dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 431-445, September.
    7. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    8. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
    9. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    10. Masuda, Takeshi, 2002. "Farsighted stability in average return games," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 169-181, November.
    11. Kawasaki, Ryo & Muto, Shigeo, 2009. "Farsighted stability in provision of perfectly "Lumpy" public goods," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 98-109, July.
    12. Yoshio Kamijo & Shigeo Muto, 2010. "Farsighted Coalitional Stability Of A Price Leadership Cartel," The Japanese Economic Review, Japanese Economic Association, vol. 61(4), pages 455-465, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hanaki, Nobuyuki & Tanimura, Emily & Vriend, Nicolaas J., 2019. "The Principle of Minimum Differentiation revisited: Return of the median voter," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 145-170.
    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. Toshiyuki Hirai, 2018. "Single-payoff farsighted stable sets in strategic games with dominant punishment strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1087-1111, November.
    4. Kawasaki, Ryo, 2015. "Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 8-12.
    5. Kawasaki, Ryo & Sato, Takashi & Muto, Shigeo, 2015. "Farsightedly stable tariffs," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 118-124.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Toshiyuki Hirai, 2018. "Single-payoff farsighted stable sets in strategic games with dominant punishment strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1087-1111, November.
    2. Kawasaki, Ryo & Sato, Takashi & Muto, Shigeo, 2015. "Farsightedly stable tariffs," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 118-124.
    3. Kawasaki, Ryo, 2015. "Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 8-12.
    4. Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2008. "Farsighted coalitional stability in TU-games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 303-313, November.
    5. Bloch, Francis & van den Nouweland, Anne, 2021. "Myopic and farsighted stable sets in 2-player strategic-form games," Games and Economic Behavior, Elsevier, vol. 130(C), pages 663-683.
    6. Effrosyni Diamantoudi & Eftichios Sartzetakis, 2015. "International environmental agreements: coordinated action under foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(3), pages 527-546, August.
    7. Yoshio Kamijo, 2013. "Stability and efficiency in perfect foresight situation," Theory and Decision, Springer, vol. 75(3), pages 339-357, September.
    8. Kawasaki, Ryo & Muto, Shigeo, 2009. "Farsighted stability in provision of perfectly "Lumpy" public goods," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 98-109, July.
    9. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Iskakov, A. & Iskakov, M., 2017. "In Search of a Generalized Concept of Rationality," Journal of the New Economic Association, New Economic Association, vol. 34(2), pages 181-189.
    11. 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.
    12. Kimya, Mert, 2020. "Equilibrium coalitional behavior," Theoretical Economics, Econometric Society, vol. 15(2), May.
    13. Iskakov, M. & Iskakov, A. & d'Aspremont, C., 2018. "Games for cautious players: The Equilibrium in Secure Strategies," Games and Economic Behavior, Elsevier, vol. 110(C), pages 58-70.
    14. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    15. Toshiyuki Hirai, 2017. "The stable set of the social conflict game with commitments: existence, uniqueness, and efficiency," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 149-166, March.
    16. Jung, Hanjoon Michael, 2009. "Spatial pillage game," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 701-707, December.
    17. Bloch, Francis & van den Nouweland, Anne, 2020. "Farsighted stability with heterogeneous expectations," Games and Economic Behavior, Elsevier, vol. 121(C), pages 32-54.
    18. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    19. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    20. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "On the number of blocks required to access the core," MPRA Paper 26578, University Library of Munich, Germany.

    More about this item

    Keywords

    Farsighted stable set; Indirect dominance; Hotelling location game; Strategic form game with no-Nash equilibrium; Coalition formation;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rut:rutres:200808. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/derutus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.