Journal of Optimization Theory and Applications

, Volume 87, Issue 3, pp 539–552 | Cite as

Teraoka-type two-person nonzero-sum silent duel

  • V. J. Baston
  • A. Y. Garnaev
Contributed Papers


The paper discusses a silent nonzero-sum duel between two players each of whom has a single bullet. The duel is terminated at a random time in [0, 1] given by a cumulative distribution function. It is shown that the game has a unique Nash equilibrium under a wide range of possible payoff values for simultaneous firing. This contrasts with a very similar game considered by Teraoka for which there are many Nash equilibria.

Key Words

Nonzero-sum games Nash equilibria games of timing silent duels 


  1. 1.
    Teraoka, Y.,A Two-Person Game of Timing with Random Termination, Journal of Optimization Theory and Applications, Vol. 40, pp. 379–396, 1983.Google Scholar
  2. 2.
    Sakaguchi, M.,Marksmanship Contests: Nonzero-Sum Game of Timing, Mathematica Japonica, Vol. 22, pp. 585–596, 1978.Google Scholar
  3. 3.
    Karlin, S.,Mathematical Methods and Theory in Games, Programming, and Economics, Vol. 2, Addison-Wesley, Reading, Massachusetts, 1959.Google Scholar
  4. 4.
    Restrepo, R.,Tactical Problems Involving Several Actions, Contributions to the Theory of Games 3, Edited by M. Dresher, A. W. Tucker, and P. Wolfe, Annals of Mathematical Studies, Princeton University Press, Princeton, New Jersey, Vol. 39, pp. 313–335, 1971.Google Scholar
  5. 5.
    Fox, M., andKimeldorf, G.,Noisy Duels, SIAM Journal on Applied Mathematics, Vol. 17, pp. 353–361, 1969.Google Scholar
  6. 6.
    Sweat, C. W.,A Single-Shot Noisy Duel with Detection Uncertainty, Operations Research, Vol. 19, pp. 170–181, 1971.Google Scholar
  7. 7.
    Hendricks, K., Weiss, A., andWilson, C.,The War of Attrition in Continuous Time with Complete Information, International Economic Review, Vol. 29, pp. 663–680, 1988.Google Scholar
  8. 8.
    Hamers, H.,A Silent Duel Over a Cake, ZOR—Mathematical Methods of Operations Research, Vol. 37, pp. 119–127, 1993.Google Scholar
  9. 9.
    Baston, V. J., andGarnaev, A. Y.,A Nonzero-Sum War of Attrition, ZOR—Mathematical Methods of Operations Research 1995 (to appear).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. J. Baston
    • 1
  • A. Y. Garnaev
    • 2
  1. 1.Department of MathematicsUniversity of SouthamptonSouthamptonEngland
  2. 2.Department of Computational MathematicsCivil Engineering InstituteSaint PetersburgRussia

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