A game locating a needle in a square haystack
type: Item
instance of: scholarly article
title: A game locating a needle in a square haystack
zbMATH Open document ID: 0584.90098
DOI: 10.1007/BF00940282
author: F. A. Bostock
author: Victor J. Baston
published in: Journal of Optimization Theory and Applications
publication date: 1986-01-01T00:00:00Z
review text: The following hider-seeker zero-sum game is considered. The hider hides a needle of length a, \(0<a\leq \sqrt{2}\), in the closed unit square, and the seeker tries to locate it by shooting in a straight line across the square. The payoff to the seeker is 1 if he hits the needle and 0 otherwise. A solution of the game is obtained when \(a\geq \sqrt{2}/2\) or when a lies in either of the intervals [\(\sqrt{5}/4\), 2-\(\sqrt{2}]\) and [\(\sqrt{2}/3\), 1/2]; in addition, it is shown that, when n is a positive integer and \(a=1/n\), the value of the game is 1/2n. The properties of the solutions are in marked contrast to those for the analogous game over the closed unit disc, which the authors solved in a previous paper [ibid. 47, 383-391 (1985; Zbl 0556.90096)], and suggest that a complete solution may well be difficult. It is also shown that every member of a whole class of haystack games has a value.
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 3936966
zbMATH Keywords: hider-seeker zero-sum game
zbMATH Keywords: closed unit square
zbMATH Keywords: value of the game
zbMATH Keywords: haystack games
zbMATH Keywords: infinite games
MaRDI profile type: Publication
cites work: A game locating a needle in a circular haystack
cites work: Q3670933
cites work: Q5613067
full work available at URL: https://doi.org/10.1007/bf00940282
OpenAlex ID: W2071653035
Recommended article: A game locating a needle in a circular haystack
Recommended article: On a square haystack game
Recommended article: Q3360686
Recommended article: A matching game
Recommended article: Search game in a rectangle
Recommended article: Some Stackelberg type location game
Recommended article: A search game with one object and two searchers
description: scientific article; zbMATH DE number 3936966