Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T15:52:52.011Z Has data issue: false hasContentIssue false
  • English
  • Français

Last round betting

Published online by Cambridge University Press:  14 July 2016

Thomas S. Ferguson  and
C. Melolidakis
Thomas S. Ferguson*
Affiliation:
University of California, Los Angeles
C. Melolidakis*
Affiliation:
Technical University of Crete
*
∗Postal address: Department of Mathematics, University of California, Los Angeles, CA 90024, USA. e-mail: [email protected]
∗∗Postal address: Department of Industrial Engineering, Technical University of Crete, Hania, 73100, Greece. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Two players with differing amounts of money simultaneously choose an amount to bet on an even-money win-or-lose bet. The outcomes of the bets may be dependent and the player who has the larger amount of money after the outcomes are decided is the winner. This game is completely analyzed. In nearly all cases, the value exists and optimal strategies for the two players that give weight to a finite number of bets are explicitly exhibited. In a few situations, the value does not exist.

Keywords

ZERO-SUM GAMEGENERALIZED SADDLE POINTJEOPARDY
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 974 - 987
Copyright
Copyright © Applied Probability Trust 1997 

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

Baston, V. J., Bostoch., F. A. and Ruckle, W. H. (1990) The gold-mine game. J. Opt. Theory Appl. 64, 641–650.Google Scholar
Fan, K. (1953) Minimax theorems. Proc. Nat. Acad. Sci. 39, 42–47.Google Scholar
Ferguson, T. S. (1967) Mathematical Statistics – A Decision-Theoretic Approach. Academic Press, New York.Google Scholar
Garnaev, A. Y. (1992) On a simple MIX game. Int. J. Game Theory 21, 237–247.Google Scholar
Gilbert, G. T. and Hatcher, R. L. (1994) Wagering in Final Jeopardy! Math. Mag. 67, 268–281.Google Scholar
Gross, O. (1950) The symmetric Blotto game. RAND Res. Memo. RM-408, 19 July.Google Scholar
Gross, O. and Wagner, R. (1950) A continuous Colonel Blotto game. RAND Res. Memo. RM-408, 17 June.Google Scholar
Heuer, G. A. (1989) Reduction of Silverman-like games to games on bounded sets. Int. J. Game Theory 18, 31–36.Google Scholar
Karlin, S. (1959) Mathematical Methods and Theory in Games, Programming and Economics. Vols I and II. Addison-Wesley, Reading, MA.Google Scholar
Kimeldorf, G. and Lang, J. P. (1978) Asymptotic properties of discrete duels. J. Appl. Prob. 15, 374–396.Google Scholar
Kurisu, T. (1991) On a duel with time lag and arbitrary accuracy functions. Int. J. Game Theory 19, 375–405.Google Scholar
Parthasarathy, T. and Raghavan, T. E. S. (1971) Some Topics in Two-Person Games. (Modern Analytic and Computational Methods in Science and Mathematics 22.) Elsevier, New York.Google Scholar
Radzik, T. (1988) Games of timing related to distribution of resources. J. Opt. Theory Appl. 58, 443–471.Google Scholar
Shapley, L. S. (1964) Some topics in two-person games. In Advances in Game Theory. ed. Dresher, M., Shapley, L. S. and Tucker, A. W. Princeton University Press, Princeton, NJ. pp. 1–28.Google Scholar
Sion, M. and Wolfe, P. (1957) On a game without a value. Ann. Math. Studies 39, 299–306.Google Scholar
Taylor, J. M. G. (1994) Betting strategies in final jeopardy. Chance 7, 14–19, 27.Google Scholar
Teraoka, Y. and Nakai, T. (1990) A game of timing which shifts stochastically from a noisy version to a silent version. J. Info. Opt. Sci. 11, 215–230.Google Scholar
Wong, S. (1992) Casino Tournament Strategy. Pi Yee Press, La Jolla, CA.Google Scholar