A two-person game of timing with random termination

  • Y. Teraoka
Contributed Papers

Abstract

We consider a marksmanship contest in which the first contestant to hit his target wins and the contest is to be terminated at a random timeT with cdfH(t). The model is evidently an extension of the classical discrete fire duel to the timing problem under an uncertain environment. It is shown that the uncertainty on the termination of the contest has influence on the equilibrium strategies and the equilibrium values.

Key Words

Noncooperative two-person games games of timing strategic information decision under random termination 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dresher, M.,Games of Strategy: Theory and Applications, Prentice Hall, Englewood Cliffs, New Jersey, 1954.Google Scholar
  2. 2.
    Fox, M., andKimeldorf, G.,Noisy Duels, SIAM Journal on Applied Mathematics, Vol. 17, pp. 353–361, 1969.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.
    Sweat, C. W.,A Single-Shot Noisy Duel with Detection Uncertainty, Operations Research, Vol. 19, pp. 170–181, 1971.Google Scholar
  5. 5.
    Teraoka, Y.,Noisy Duel with Uncertain Existence of the Shot, International Journal of Game Theory, Vol. 5, pp. 239–249, 1976.Google Scholar
  6. 6.
    Teraoka, Y.,Silent-Noisy Duel with Uncertain Existence of the Shot, Bulletin of Mathematical Statistics, Vol. 18, pp. 43–52, 1981.Google Scholar
  7. 7.
    Teraoka, Y.,A Two-Person Game of Timing with Random Arrival Time of the Object, Mathematica Japonica, Vol. 24, pp. 427–438, 1979.Google Scholar
  8. 8.
    Styszyński, S.,A Silent-Silent Duel with Bullets Accessible at Random Moments, Politechniki Wroclawskiej, Instytut Matematyki, Research Report No. 40, 1979.Google Scholar
  9. 9.
    Kurisu, T.,On a Noisy-Silent versus Silent Duel with Equal Accuracy Functions, Journal of Optimization Theory and Applications (to appear).Google Scholar
  10. 10.
    Epstein, R. A.,The Theory of Gambling and Statistical Logic, Academic Press, New York, New York, 1977.Google Scholar
  11. 11.
    Sakaguchi, M.,Marksmanship Contests—Nonzero Some Game of Timing, Mathematica Japonica, Vol. 22, pp. 585–596, 1978.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Y. Teraoka
    • 1
  1. 1.Department of Applied MathematicsHimeji Institute of TechnologyHimejiJapan

Personalised recommendations