Success probabilities for second guessers

Success probabilities for second guessers

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...

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Veröffentlicht in:Journal of applied probability 1980-12, Vol.17 (4), p.1133-1137
1. Verfasser: Pittenger, A. O.
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Sprache:eng
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Mathematical objects
Short Communications
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creator Pittenger, A. O.
description 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.
doi_str_mv 10.2307/3213227
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source JSTOR; JSTOR Mathematics & Business
subjects Mathematical objects
Short Communications
title Success probabilities for second guessers
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