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Optimal search for a small (or well hidden) object

Wednesday 23 October 2013, 4.30pm-6pm
NAB 2.06, New Academic Building

Dr Thomas Lidbetter

LSE Fellow

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In traditional models of search games, an immobile Hider picks a point in some search space and a Searcher picks a constant speed trajectory in the space with the aim of minimising the expected time to reach the Hider.  However, in practice a Searcher's ability to detect a Hider may depend on the speed at which he is travelling.  For example, when searching for a contact lens there are two possible modes of travel: a fast walking speed and a slow searching speed.  Equally, an explosives expert searching for an IED may be able to move from place to place quickly in a vehicle, but in order to detect the IEDs he must get out of his vehicle and move at a slower pace.  Hence we adapt the traditional model to allow the Searcher to move at either a slow speed at which he is able to detect the Hider, or a fast speed at which he cannot.  We view this as a zero sum game and show that the solution of the game is complicated even if it is played on a single arc.  We give the solution to this, and to the game played on trees and other networks.  We also consider what happens if the Searcher is able to detect the Hider with a small probability when he is travelling at the fast speed.


 Thomas Lidbetter