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The gold-mine game

  • V. J. Baston
  • F. A. Bostock
  • W. H. Ruckle
Technical Note

Abstract

The paper considers the following two-person zero-sum game. The minimizing player chooses to hide his gold and a mine in two distinct boxes from an infinite number of boxes labelled 1, 2, 3,.... The maximizing player now chooses to open the boxes in some order, and if he finds the gold before the mine the payoff to him is 1; otherwise, the payoff is zero. The game is solved in the sense of Kindler.

Key Words

Two-person zero-sum games finitely additive strategies search games 

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References

  1. 1.
    Karlin, S.,Mathematical Methods and Theory in Games, Programming, and Economics, Vol. 2: Theory of Infinite Games, Pergamon Press, New York, New York, 1959.Google Scholar
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    Karlin, S.,Operator Treatment of Minimax Principle, Contributions to the Theory of Games 1, Edited by H. W. Kuhn and A. W. Tucker, Annals of Mathematical Studies, Vol. 24, pp. 133–154, 1950.Google Scholar
  3. 3.
    Fenstad, J. E.,Good Strategies in General Games, Mathematische Zeitschrift, Vol. 101, pp. 322–330, 1967.Google Scholar
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    Kindler, J.,A General Solution Concept for Two-Person Zero-Sum Games, Journal of Optimization Theory and Applications, Vol. 40, pp. 105–119, 1983.Google Scholar
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    Yanovskaya, E. B.,The Solution of Infinite Zero-Sum Two-Person Games with Finitely Additive Strategies, Theory of Probability and Its Applications, Vol. 15, pp. 153–158, 1970.Google Scholar
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    Clarke, L. E.,Random Variables, Longman, London, England, 1975.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. J. Baston
    • 1
  • F. A. Bostock
    • 1
  • W. H. Ruckle
    • 2
  1. 1.Faculty of Mathematical StudiesUniversity of SouthamptonSouthamptonEngland
  2. 2.Department of Mathematical SciencesClemson UniversityClemson

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