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EQUILIBRIUM IN n-PERSON GAME OF SHOWCASE SHOWDOWN

Published online by Cambridge University Press:  23 April 2010

Vladimir Mazalov  and
Anna Ivashko
Vladimir Mazalov
Affiliation:
Institute of Applied Mathematical Research, Karelian Research Center of RAS, Petrozavodsk, Russia E-mail: vmazalov@krc.karelia.ru, afalko@krc.karelia.ru
Anna Ivashko
Affiliation:
Institute of Applied Mathematical Research, Karelian Research Center of RAS, Petrozavodsk, Russia E-mail: vmazalov@krc.karelia.ru, afalko@krc.karelia.ru
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Abstract

In this article we consider a noncooperative n-person optimal stopping game of Showcase Showdown, in which each player observes the sum of independent and identically distributed random variables uniformly distributed in [0, 1]. Players can decide to stop the draw in each moment. The objective of a player is to get the maximal number of scores that does is not exceeded level 1. If the scores of all players exceed 1, then the winner is the player whose score is closest to 1. We derive the equilibrium in this game on the basis of the dynamic programming approach.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 3 , July 2010 , pp. 397 - 403
Copyright
Copyright © Cambridge University Press 2010

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References

1.Chow, Y.S., Robbins, H. & Siegmund, D. (1971). Great expectations: The theory of optimal stopping. Boston: Houghton Mifflin.Google Scholar
2.Coe, P.R. & Butterworth, W. (1995). Optimal stopping in “The Showcase Showdown,” The American Statistician 49: 271–275.Google Scholar
3.Kaynar, B. (2009). Optimal stopping in a stochastic game. Probability in the Engeneering and Information Sciences 23: 51–60.CrossRefGoogle Scholar
4.Mazalov, V.V. (1996). A game related to optimal stopping of two sequences of independent random variables having different distributions. Mathematica Japonica 43(1): 121–128.Google Scholar
5.Sakaguchi, M. (2005). Equilibrium in two-player games of “Showcase Showdown.” Scientiae Mathematicae Japonicae 61: 145–151.Google Scholar
6.Sakaguchi, M. (2007). Players’ information in two-player games of “Score Showdown.” In Petrosjan, L. and Mazalov, V. (eds). Game theory and applications, Petrosjan, L. and Mazalov, V. (eds). New York: Nova Science. pp. 111–124.Google Scholar
7.Tijms, H.C. (2007). Understanding probability, 2nd ed. Cambridge: Cambridge University Press.CrossRefGoogle Scholar