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Lion and man—can both win?

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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.

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Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB, UK

    B. Bollobás & I. Leader

  2. Department of Mathematics, University of Memphis, Dunn Hall, 3725 Noriswood, Memphis, TN, 38152, USA

    B. Bollobás

  3. Department of Mathematics, Queen Mary University of London, London, E1 4NS, UK

    M. Walters

Authors
  1. B. Bollobás
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  2. I. Leader
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  3. M. Walters
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Correspondence to B. Bollobás.

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Bollobás, B., Leader, I. & Walters, M. Lion and man—can both win?. Isr. J. Math. 189, 267–286 (2012). https://doi.org/10.1007/s11856-011-0158-6

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  • DOI: https://doi.org/10.1007/s11856-011-0158-6

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