The Theory of Search Games and Rendezvous
Search Theory is one of the original disciplines within the field of Operations Research. It deals with the problem faced by a Searcher who wishes to minimize the time required to find a hidden object, or “target. ” The Searcher chooses a path in the “search space” and finds the target when he is sufficiently close to it. Traditionally, the target is assumed to have no motives of its own regarding when it is found; it is simply stationary and hidden according to a known distribution (e. g. , oil), or its motion is determined stochastically by known rules (e. g. , a fox in a forest). The problems dealt with in this book assume, on the contrary, that the “target” is an independent player of equal status to the Searcher, who cares about when he is found. We consider two possible motives of the target, and divide the book accordingly. Book I considers the zero-sum game that results when the target (here called the Hider) does not want to be found. Such problems have been called Search Games (with the “ze- sum” qualifier understood). Book II considers the opposite motive of the target, namely, that he wants to be found. In this case the Searcher and the Hider can be thought of as a team of agents (simply called Player I and Player II) with identical aims, and the coordination problem they jointly face is called the Rendezvous Search Problem.
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Search Trajectories Search in a Multidimensional Region 3 7 1 Inhomogeneous search spaces 4 Search for a Mobile Hider 4 1 4 2 4 3 4 4 4 5 Introd...
Rendezvous Strategies Outline of Book II 11 Elementary Results and Examples
The Symmetric Rendezvous Value Rs Properties of Optimal Strategies and Rendezvous Values 13 Rendezvous on Labeled Networks
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A–F strategy agents algorithm Alpern and Beck Alternating Search alternation rule arcs assume assumption asymmetric rendezvous problem asymmetric rendezvous value Baston bound Chapter choose clockwise common notion complete graph Consequently consider cost function cumulative distribution function cycle graph defined density distribution F DLSP equiprobably equivalent Eulerian Eulerian path expected capture expected meeting finite given graph H-network Hamiltonian path hider hiding strategy immobile hider initial distance initial distribution initial location integer interval least expected Lemma length Let denote Linear Search Problem lower semicontinuous maximum speed minimax theorem mixed strategy MWFM node notion of direction obtained optimal strategy pair origin pair f path period player-symmetric probability distribution Proof pure strategy rendezvous search rendezvous strategies rendezvousers result satisfies search game search region search space search trajectory searcher Section solution starting point strategy f symmetry group Theorem uniform distribution uniformly optimal unit speed Wait For Mommy