Lion and Man -- Can Both Win? Export

@article{citeulike:5785206, 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.}, archivePrefix = {arXiv}, author = {Bollob\'{a}s, B. and Leader, I. and Walters, M.}, citeulike-article-id = {5785206}, citeulike-linkout-0 = {http://arxiv.org/abs/0909.2524}, citeulike-linkout-1 = {http://arxiv.org/pdf/0909.2524}, day = {14}, eprint = {0909.2524}, keywords = {article, gametheory, graphtheory, optimization}, month = {Sep}, posted-at = {2009-09-15 19:40:05}, priority = {2}, title = {Lion and Man \&\#45;\&\#45; Can Both Win?}, url = {http://arxiv.org/abs/0909.2524}, year = {2009} }

TY - JOUR ID - citeulike:5785206 L3 - citeulike-article-id:5785206 N2 - 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. TI - Lion and Man -- Can Both Win? KW - article KW - gametheory KW - graphtheory KW - optimization AU - Bollobás, B AU - Leader, I AU - Walters, M PY - 2009/Sep/14/ UR - http://arxiv.org/abs/0909.2524 ER -