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Asymptotic properties of non-discrete duels

Published online by Cambridge University Press:  14 July 2016

George Kimeldorf
Affiliation:
University of Texas at Dallas
John Patrick Lang
Affiliation:
Old Dominion University, Norfolk, Virginia

Abstract

For fixed accuracy functions, let Gnm be a non-discrete duel in which the amounts of ammunition available to the two players are n and m, respectively. Let vnm be the value of Gnm and let the support of the optimal pure strategies for the players be (anm, 1). The asymptotic relationships among the quantities n, m, vnm and anm are investigated.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[2] Fox, M. and Kimeldorf, G. (1969) Noisy duels. SIAM J. Appl. Math. 17, 353361.Google Scholar
[3] Fox, M. and Kimeldorf, G. (1970) Values and shooting times in noisy duels. J. Amer. Statist. Assoc. 65, 422430.Google Scholar
[4] Karlin, S. (1959) Mathematical Methods and Theory in Games, Programming, and Economics, II. Addison-Wesley, Reading, Mass.Google Scholar
[5] Lang, J. P. and Kimeldorf, G. (1975) Duels with continuous firing. Management Sci. 22, 470476.Google Scholar
[6] Lang, J. P. and Kimeldorf, G. (1976) Silent duels with non-discrete firing. SIAM J. Appl. Math. 31, 99110.Google Scholar
[7] Restrepo, R. (1957) Tactical problems involving several actions. Contributions to the theory of games, III. Ann. Math. Studies 39, 313335.Google Scholar
[8] Smith, G. (1967) A duel with silent-noisy gun versus noisy gun. Colloq. Math. 17, 131146.Google Scholar
[9] Styszynski, A. (1974) An n-silent-vs.-noisy duel with arbitrary accuracy functions. Zastos. Mat. 14, 205225.Google Scholar