Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-25T01:34:04.320Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic properties of discrete duels

Published online by Cambridge University Press:  14 July 2016

George Kimeldorf  and
John Patrick Lang
George Kimeldorf
Affiliation:
University of Texas at Dallas
John Patrick Lang
Affiliation:
Old Dominion University, Norfolk, Virginia
Get access Rights & Permissions [Opens in a new window]

Abstract

For fixed accuracy functions, let Gnm be a discrete-fire (silent, noisy, or silent-noisy) duel in which the amounts of ammunition available to the two players are n and m, respectively. As n and m both become large, a class of ‘ε -optimal' pure strategies (with support (anm, 1)) is derived. If vnm denotes the value of Gnm, the asymptotic relationships among the quantities n, m, vnm, and anm are investigated.

Keywords

DUELSGAMES OF TIMING
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 374 - 383
Copyright
Copyright © Applied Probability Trust 1978 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Eisen, M. (1969) Introduction to Mathematical Probability Theory. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
Fox, M. and Kimeldorf, G. (1969) Noisy duels. SIAM J. Appl. Maths 17, 353–361.Google Scholar
Fox, M. and Kimeldorf, G. (1970) Values and shooting times in noisy duels. J. Amer. Statist. Assoc. 65, 422–430.Google Scholar
Kimeldorf, G. and Lang, J. P. (1977) Asymptotic properties of non-discrete duels. J. Appl. Prob. 14, 153–161.Google Scholar
Lang, J. P. and Kimeldorf, G. (1975) Duels with continuous firing. Management Sci. 22, 470–476.Google Scholar
Lang, J. P. and Kimeldorf, G. (1976) Silent duels with non-discrete firing. SIAM J. Appl. Maths 31, 99–110.Google Scholar
Restrepo, R. (1957) Tactical problems involving several actions. Contributions to the theory of games, III. Ann. Math. Studies 39, 313–335.Google Scholar
Smith, G. (1967) A duel with silent-noisy gun versus noisy gun. Colloq. Math. 17, 131–146.Google Scholar
Styszynski, A. (1974) An n-silent versus noisy duel with arbitrary accuracy functions. Zast. Mat. 14, 205–225.Google Scholar