Search games and other applications of game theory
The author presents a number of applications of game theory along with the background of the games that occur in these applications. He also presents a list of unsolved problems. The lecture notes are organized in six chapters. The first chapter presents the preliminary concepts and results from game theory. The second chapter is on ambush games which discusses the infiltration games in which an intruder knows the length of an invisible electric cable used by a guard to protect a channel against infiltration. The guard chooses an interval consisting of \(m\) integer points, \(m < n \), in the interval \([1,n]\) which is to be protected, and the infiltrator chooses his point of crossing in \([1,n].\) With a suitable payoff one can formulate a zero-sum game to describe this situation. This chapter analyses this game and its generalization, the matrix search game. Also considered are related games like the helicopter versus submarine games. Chapter 3 presents allocation games in which a player searching his or her hiding opponent has to decide the allocation of a total search effort \(X\) to each of the \(n\) points where the opponent may be hidden. This situation with suitable assumptions regarding the probability of success at each point depending on the effort allocated, can be modelled as a game. Chapter 4 discusses this game (with and without search costs) and its variants. This chapter also discusses marketing games with and without taking into account expenses. Chapter 5 discusses games of timing like duels and games of research and development which studies the strategic aspects of production development in manufacturing by means of a game model. Chapter six discusses parlour games. Thus this book presents an interesting approach to game theory where the model situations are introduced first and the development of theory follows from an analysis of the model. Some related books are: \textit{S. Gal}, Search games. Academic Press, New York (1980; Zbl 0439.90102) and \textit{W. H. Ruckle}, Geometric games and their applications. Pitman, Boston (1983; Zbl 0519.90096).
scientific article; zbMATH DE number 1482947