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A Location Game On Disjoint Circles

Author

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  • 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
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    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.

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    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

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