Lion and man-can both win?

Abstract

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. © 2012 Hebrew University Magnes Press.

Publication Title

Israel Journal of Mathematics

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