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Success probabilities for second guessers

Published online by Cambridge University Press:  14 July 2016

A. O. Pittenger
A. O. Pittenger*
Affiliation:
University of Maryland Baltimore County
*
∗Postal address: Department of Mathematics, University of Maryland Baltimore County, Catonsville, MD 21228, U.S.A.
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Abstract

Two people independently and with the same distribution guess the location of an unseen object in n-dimensional space, and the one whose guess is closer to the unseen object is declared the winner. The first person announces his guess, but the second modifies his unspoken idea by moving his guess in the direction of the first guess and as close to it as possible. It is shown that if the distribution of guesses is rotationally symmetric about the true location of the unseen object, ¾ is the sharp lower bound for the success probability of the second guesser. If the distribution is fixed and the dimension increases, then for a certain class of distributions, the success probability approaches 1.

Keywords

SECOND GUESSERS
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1133 - 1137
Copyright
Copyright © Applied Probability Trust 

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References

Helms, L. L. (1969) Introduction to Potential Theory. Wiley-Interscience, New York.Google Scholar
Steele, J. M. and Zidek, J. (1980) Optimal strategies for second guessers. J. Amer. Statist. Assoc. CrossRefGoogle Scholar