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A search game is a two-person zero-sum game which takes place in a set called the search space. The searcher can choose any continuous trajectory subject to a maximal velocity constraint. It is always assumed that neither the searcher nor the hider has any knowledge about the movement of the other player until their distance apart is less than or equal to the discovery radius and at this very moment capture occurs. As mathematical models, search games can be applied to areas such as hide-and-seek games that children play or representations of some tactical military situations. The area of search games was introduced in the last chapter of Rufus Isaacs' classic book "Differential Games" and has been developed further by Shmuel Gal and Steve Alpern. The princess and monster game deals with a moving target.
Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers.
Chases and Escapes: The Mathematics of Pursuit and Evasion is a mathematics book on continuous pursuit–evasion problems. It was written by Paul J. Nahin, and published by the Princeton University Press in 2007. It was reissued as a paperback reprint in 2012. The Basic Library List Committee of the Mathematical Association of America has rated this book as essential for inclusion in undergraduate mathematics libraries.
References
- ↑ Becker, A. T., & Garcia, J. (2018, January 22). Wolfram Demonstrations Project. The Homicidal Chauffeur Problem. https://demonstrations.wolfram.com/TheHomicidalChauffeurProblem/
- ↑ R. Isaacs, Games of Pursuit, RAND Corporation (1951)
- ↑ R. Isaacs, Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, John Wiley & Sons, New York (1965), PP 349–350.