The Theory of Search Games and Rendezvous

1. Front Matter

   Pages i-xv

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2. Search Games

   1. Front Matter

      Pages 1-1

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   2. Introduction to Search Games

      Pages 3-6

3. Search Games in Compact Spaces

   1. Front Matter

      Pages 7-7

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   2. General Framework

      Pages 9-12

   3. Search for an Immobile Hider

      Pages 13-43

   4. Search for a Mobile Hider

      Pages 45-77

   5. Miscellaneous Search Games

      Pages 79-97

4. Search Games in Unbounded Domains

   1. Front Matter

      Pages 99-99

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   2. General Framework

      Pages 101-105

   3. On Minimax Properties of Geometric Trajectories

      Pages 107-122

   4. Search on the Infinite Line

      Pages 123-144

   5. Star and Plan Search

      Pages 145-162

5. Rendezvous Search

   1. Front Matter

      Pages 163-163

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   2. Introduction to Rendezvous Search

      Pages 165-172

   3. Elementary Results and Examples

      Pages 173-178

6. Rendezvous Search on Compact Spaces

   1. Front Matter

      Pages 179-179

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   2. Rendezvous Values of a Compact Symmetric Region

      Pages 181-189

   3. Rendezvous on Labeled Networks

      Pages 191-205

   4. Asymmetric Rendezvous on an Unlabeled Circle

      Pages 207-221

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.

• Finite
• Mathematica
• economics
• graph
• theorem

• London School of Economics, UK

  Steve Alpern

• University of Haifa, Israel

  Shmuel Gal

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