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SUMMARY:Searching for Multiple Hidden Objects - Thomas Lidbetter (LSE)
DTSTART:20120611T140000Z
DTEND:20120611T150000Z
UID:TALK38231@talks.cam.ac.uk
CONTACT:Felix Fischer
DESCRIPTION:Suppose k objects are hidden amongst n>k boxes\, each with a d
 esignated search cost.  A Searcher pays to open the boxes one by one until
  all the objects have been found.  We consider this as a zero-sum game bet
 ween the Searcher who wishes to minimise the total search cost and a malev
 olent Hider.  We show that it is optimal for the objects to be hidden in a
  subset A of k boxes with probability proportional to the product p(A) of 
 the search costs of those boxes.  It is optimal for the Searcher to begin 
 by opening a subset A of k boxes with probability p(A)\, and then search t
 he remaining boxes in a random order.  We show how this game can be consid
 ered as specific example of a wider class of search games for multiple obj
 ects on a network\, and we give the solution of the game for 2-arc-connect
 ed networks (networks that cannot be disconnected by removing fewer than 2
  arcs).
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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