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In a search game, two players are placed in a dark search arena A and
move about until the first time T that they meet. If A is a network,
meeting is simply being at the same location; if A is a region of
space, meeting is being sufficiently close. In a game of
hide-and-seek, the Searcher wishes to minimize T while the Hider
wishes to maximize T. In rendezvous search, both players are
minimizers. Hide-and-seek comes in two flavors: the Hider can be
mobile (e.g. search for Bin Laden) or immobile (search for a
bomb). Rendezvous search also comes in two flavors, depending on
whether or not the players can agree beforehand which roles they will
take. For example if A is a circle the asymmetric version allows the
strategy pair [clockwise, counter-clockwise], which is optimal. In the
symmetric version, which is unsolved, this strategy pair is not
available. The symmetric rendezvous problem on the line, with a known
initial distance between the players, is also an unsolved
problem. Recent work with P. Leone allows rendezvous to take place, in
addition to when meeting, when one player finds a 'gift' left by the
other (water bottle when lost in the desert).
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