Lion and man-can both win?

被引：13

作者：

Bollobas, B. ^{[1
,2
]}

Leader, I. ^{[1
]}

Walters, M. ^{[3
]}

机构：

[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England

[2] Univ Memphis, Dept Math, Memphis, TN 38152 USA

[3] Queen Mary Univ London, Dept Math, London E1 4NS, England

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2012年 / 189卷 / 01期

基金：

美国国家科学基金会;

关键词：

Winning Strategy; Closed Disc; Full Speed; Closed Unit Disc; Drawing Strategy;

D O I：

10.1007/s11856-011-0158-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with continuous-time pursuit and evasion games. Typically, we have a lion and a man in a metric space: they have the same speed, and the lion wishes to catch the man while the man tries to evade capture. We are interested in questions of the following form: is it the case that exactly one of the man and the lion has a winning strategy? As we shall see, in a compact metric space at least one of the players has a winning strategy. We show that, perhaps surprisingly, there are examples in which both players have winning strategies. We also construct a metric space in which, for the game with two lions versus one man, neither player has a winning strategy. We prove various other (positive and negative) related results, and pose some open problems.

引用

页码：267 / 286

页数：20

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