A generalization of Ruckle's results for an ambush game
type: Item
instance of: scholarly article
title: A generalization of Ruckle's results for an ambush game
zbMATH Open document ID: 0982.91006
DOI: 10.1016/S0377-2217(99)00137-X
author: Noemí Zoroa
author: Procopio Zoroa
author: María-José Fernández-Sáez
published in: European Journal of Operational Research
publication date: 2002-04-11T00:00:00Z
review text: Consider the following 2-person 0-sum normal form game. Player 1 picks a point on \([0,1]\). Simultaneously, player 2 picks two obstacles (intervals of length \(a\) and \(b\), respectively). Player 1 wins (gets payoff \(=+1\)) if the point he or she picked is in neither of player 2's intervals. Let \(k\) be an integer and suppose the following: \(0< a< b< 1/2\), \(kb< 1\leq (k+1)b\). Then for the case \(kb+a\geq 1\) the paper finds conditions under which the value of the game exists and can be expressed in closed form. In particular, the value to player 1 is increasing in \(k\). The results in this paper considerably extend those of \textit{W. H. Ruckle} [Geometric games and their applications, Boston, Pitman (1983; Zbl 0519.90096)].
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 90B40
zbMATH DE Number: 1358202
zbMATH Keywords: ambush game
zbMATH Keywords: Ruckle's problem
zbMATH Keywords: 2-person zero-sum normal form game
MaRDI profile type: Publication
cites work: A continuous game of ambush
cites work: On a ruckle problem in discrete games of ambush
cites work: The discrete evasion game with three-move lag
cites work: Q3670933
full work available at URL: s0377-2217(99)00137-x
OpenAlex ID: W2010124803
description: scientific article; zbMATH DE number 1358202