IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v11y2009i04ns021919890900239x.html
   My bibliography  Save this article

A Location Game On Disjoint Circles

Author

Listed:
  • MARCIN DZIUBIŃSKI

    (Institute of Informatics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland)

  • DEBABRATA DATTA

    (Institute of Management Technology, Raj Nagar, Post Box No. 137, Ghaziabad 201001, India)

  • JAIDEEP ROY

    (Department of Economics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK)

Abstract

Two players are endowed with resources for setting upNlocations onKidentical circles, withN > K ≥ 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. They face a resource mobility constraint such that not allNlocations can be placed in the first round. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that forK = 1, the second mover always has a winning strategy in this game. In this paper we show that withK > 1, the second mover advantage disappears as in this case both players have a tying strategy. We also study a natural variant of this game where the resource mobility constraint is more stringent so that in each round each player chooses a single location where we show that the second mover advantage re-appears. We suggest some Nash equilibrium configurations of locations in both versions of the game.

Suggested Citation

  • Marcin Dziubiński & Debabrata Datta & Jaideep Roy, 2009. "A Location Game On Disjoint Circles," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 391-406.
    • Handle: RePEc:wsi:igtrxx:v:11:y:2009:i:04:n:s021919890900239x
    DOI: 10.1142/S021919890900239X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021919890900239X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021919890900239X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. , & ,, 2006. "Group formation and voter participation," Theoretical Economics, Econometric Society, vol. 1(4), pages 461-487, December.
    2. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    3. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
    4. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    5. Edward H. Chamberlin, 1953. "The Product as an Economic Variable," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 67(1), pages 1-29.
    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. Marcin Dziubiński, 2011. "Location game on disjoint line segments," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 231-262, May.
    2. Marcin Konrad Dziubinski, 2008. "Voronoi game on disjoint open curves," Working Papers 591829, Lancaster University Management School, Economics Department.

    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. Marcin Konrad Dziubinski, 2008. "Voronoi game on disjoint open curves," Working Papers 591829, Lancaster University Management School, Economics Department.
    2. Pierre Picard & Takatoshi Tabuchi, 2010. "Self-organized agglomerations and transport costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 565-589, March.
    3. Gillian Hadfield & Eric Talley, "undated". "On Public versus Private Provision of Corporate Law," American Law & Economics Association Annual Meetings 1063, American Law & Economics Association.
    4. Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
    5. Carlos Gutiérrez-Hita & Martin Peitz, 2001. "Retailer Locations, Local Supply And Price Policies," Working Papers. Serie AD 2001-26, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Hehenkamp, Burkhard & Wambach, Achim, 2010. "Survival at the center--The stability of minimum differentiation," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 853-858, December.
    7. Zhou, Dongsheng & Vertinsky, Ilan, 2001. "Strategic location decisions in a growing market," Regional Science and Urban Economics, Elsevier, vol. 31(5), pages 523-533, September.
    8. repec:ebl:ecbull:v:3:y:2007:i:30:p:1-15 is not listed on IDEAS
    9. Ralph M. Braid, 2014. "Search costs decrease prices in a model of spatial competition," Papers in Regional Science, Wiley Blackwell, vol. 93(1), pages 125-139, March.
    10. Luca Lambertini & Raimondello Orsini, 2013. "On Hotelling's ‘stability in competition’ with network externalities and switching costs," Papers in Regional Science, Wiley Blackwell, vol. 92(4), pages 873-883, November.
    11. Peitz, Martin, 1999. "The circular road revisited: Uniqueness and supermodularity," Research in Economics, Elsevier, vol. 53(4), pages 405-420, December.
    12. Helge Sanner, 2005. "Price Responses to Market Entry With and Without Endogenous Product Choice," Volkswirtschaftliche Diskussionsbeiträge 81, Universität Potsdam, Wirtschafts- und Sozialwissenschaftliche Fakultät.
    13. Vermeulen, Ben & La Poutré, Han & de Kok, Ton, 2012. "Dynamics and equilibria under incremental horizontal differentiation on the Salop circle," MPRA Paper 51449, University Library of Munich, Germany.
    14. Marta Risueño & Hamid Hamoudi, 2007. "A synthesis of location models," Economics Bulletin, AccessEcon, vol. 3(30), pages 1-15.
    15. Hinloopen, Jeroen & van Marrewijk, Charles, 1999. "On the limits and possibilities of the principle of minimum differentiation1," International Journal of Industrial Organization, Elsevier, vol. 17(5), pages 735-750, July.
    16. Marcin Dziubiński, 2011. "Location game on disjoint line segments," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 231-262, May.
    17. Król, Michał, 2012. "Product differentiation decisions under ambiguous consumer demand and pessimistic expectations," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 593-604.
    18. Alain Egli, 2005. "Hotelling's Beach with Linear and Quadratic Transportation Costs: Existence of Pure Strategy Equilibria," Diskussionsschriften dp0509, Universitaet Bern, Departement Volkswirtschaft.
    19. Toshihiro Matsumura & Noriaki Matsushima, 2010. "Patent licensing, bargaining, and product positioning," ISER Discussion Paper 0775, Institute of Social and Economic Research, Osaka University.
    20. Corchón Luis Carlos & Zudenkova Galina, 2013. "The Welfare Effects of Location and Quality in Oligopoly," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 13(2), pages 1143-1178, July.
    21. Samahita Margaret, 2020. "Pay-What-You-Want in Competition," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 20(1), pages 1-16, January.

    More about this item

    Keywords

    Competitive locations; disjoint spaces; Winning/Tying strategies; equilibrium configurations; C72; D21; D72;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    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:wsi:igtrxx:v:11:y:2009:i:04:n:s021919890900239x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.