The Theory of Search Games and Rendezvous / Edition 1
The Theory of Search Games and Rendezvous widens the dimensions to the classical problem with the addition of an independent player of equal status to the searcher, who cares about being found or not being found. These multiple motives of searcher and hider are analytically and mathematically considered in the book's two foci: Search Games (Book I) and Rendezvous Theory (Book II). Shmuel Gal's work on Search Games (Gal, 1980) stimulated considerable research in a variety of fields including Computer Science, Engineering, Biology, and Economics. Steve Alpern's original formulation of the rendezvous search problem in 1976 and his formalization of the continuous version (Alpern, 1995) have led to much research in rendezvous theory in the past few years. New material is covered in both Search Games (Book I) and Rendezvous Theory (Book II). The book examines a whole variety of new configurations of theory and problems that arise from these two aspects of the analysis - resulting in a penetrating state-of-the-art treatment of this highly useful mathematical, analytical tool.
Preface. Frequently Used Notations. Acknowledgement. Book I: Search Games. 1. Introduction to Search Games. Part One: Search Games in Compact Spaces. 2. General Framework. 3. Search for an Immobile Hider. 4. Search for a Mobile Hider. 5. Miscellaneous Search Games. Part Two: Search Games in Unbounded Domains. 6. General Framework. 7. On Minimax Properties of Geometric Trajectories. 8. Search on the Infinite Line. 9. Star and Plan Search. Book II: Rendezvous Theory. 10. Introduction to Rendezvous Search. 11. Elementary Results and Samples. Part Three: Rendezvous Search on Compact Spaces. 12. Rendezvous Values of a Compact Symmetric Region. 13. Rendezvous on Labeled Networks. 14. Asymmetric Rendezvous on an Unlabeled Circle. 15. Rendezvous on a Graph. Part Four: Rendezvous Search on Unbounded Domains. 16. Asymmetric Rendezvous on the Line (ARPL). 17. Other Rendezvous Problems on the Line. 18. Rendezvous in Higher Dimensions. Appendices. A: A Minimax Theorem for Zero-Sum Games. B: Theory of Alternating Search. C: Rendezvous-Evasion Problems. Bibliography. Index.