Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-02-11T01:57:21.630Z Has data issue: false hasContentIssue false
  • English
  • Français

THE MULTIPLE-PLAYER ANTE ONE GAME

Published online by Cambridge University Press:  17 May 2011

Sheldon M. Ross
Sheldon M. Ross
Affiliation:
Department of Industrial and System Engineering, University of Southern California, Los Angeles, CA 90089 E-mail: smross@usc.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Consider a group of players playing a sequence of games. There are k players, having arbitrary initial fortunes. Each game consists of each remaining player putting 1 in a pot, which is then won (with equal probability) by one of them. Players whose fortunes drop to 0 are eliminated. Let T(i) be the number of games played by i, and let T=max iT(i). For the case k=3, martingale stopping theory can be used to derive E[T] and E[T(i)]. When k>3, we obtain upper bounds on E[T] and, in the case in which all players have the same initial fortune, on E[T(i)]. Efficient simulation methods for estimating E[T] and E[T(i)] are discussed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 3 , July 2011 , pp. 343 - 353
Copyright
Copyright © Cambridge University Press 2011

References

REFERENCES

1.Amano, K., Tromp, J., Vitanyi, P. & Watanabe, O. (2001). Approximation, randomization, and combinatorial optimization, 5th international workshop on randomized and approximation techniques in computer science, RANDOM 2001. Lecture Notes in Computer Science, Vol. 2129, Berlin; Springer-Verlag, pp. 181–191.Google Scholar
2.Bach, E. (2007). Bounds for the expected duration of the monopolist game. Information Processing Letters 101: 86–92.CrossRefGoogle Scholar
3.Engel, A. (1993). The computer solves the three tower problem. American Mathematical Monthly 100(1): 62–64.CrossRefGoogle Scholar