Two-person zero-sum game theory deals with situations that are perfectly competitive—there are exactly two decision makers for whom there is no possibility of cooperation or compromise. It is the most fundamental part of game theory, and the part most commonly applied. There are diverse applications to military battles, sports, parlor games, economics and politics. The theory was born in World War II, and has by now matured into a significant and tractable body of knowledge about competitive decision making. The advent of modern, powerful computers has enabled the solution of many games that were once beyond computational reach. Two-Person Zero-Sum Games, 4th Ed. offers an up-to-date introduction to the subject, especially its computational aspects. Any finite game can be solved by the brute force method of enumerating all possible strategies and then applying linear programming. The trouble is that many interesting games have far too many strategies to enumerate, even with the aid of computers. After introducing ideas, terminology, and the brute force method in the initial chapters, the rest of the book is devoted to classes of games that can be solved without enumerating every strategy. Numerous examples are given, as well as an extensive set of exercises. Many of the exercises are keyed to sheets of an included Excel workbook that can be freely downloaded from the SpringerExtras website. This new edition can be used as either a reference book or as a textbook.

Clear, accessible treatment of mathematical models for resolving conflicts in politics, economics, war, business, and social relationships. Topics include strategy, game tree and game matrix, and much more. Minimal math background required. 1970 edition.

Two-person zero-sum game theory deals with situations that are perfectly competitive—there are exactly two decision makers for whom there is no possibility of cooperation or compromise. It is the most fundamental part of game theory, and the part most commonly applied. There are diverse applications to military battles, sports, parlor games, economics and politics. The theory was born in World War II, and has by now matured into a significant and tractable body of knowledge about competitive decision making. The advent of modern, powerful computers has enabled the solution of many games that were once beyond computational reach. Two-Person Zero-Sum Games, 4th Ed. offers an up-to-date introduction to the subject, especially its computational aspects. Any finite game can be solved by the brute force method of enumerating all possible strategies and then applying linear programming. The trouble is that many interesting games have far too many strategies to enumerate, even with the aid of computers. After introducing ideas, terminology, and the brute force method in the initial chapters, the rest of the book is devoted to classes of games that can be solved without enumerating every strategy. Numerous examples are given, as well as an extensive set of exercises. Many of the exercises are keyed to sheets of an included Excel workbook that can be freely downloaded from the SpringerExtras website. This new edition can be used as either a reference book or as a textbook.

This text opens with the theory of 2-person zero-sum games, 2-person non-zero sum games, and n-person games, at a level between non-mathematical introductory books and technical mathematical game theory books. Includes introductory explanations of gaming and meta games. Includes numerous exercises anbd problems with solutions and over 30 illustrations. 1986 edition.

The structure of a Silverman game can be explained very quickly: Each of two players independently selects a number out of a prede termined set, not necessarily the same one for both of them. The higher number wins unless it is at least k times as high as the other one; if this is the case the lower number wins. The game ends in a draw if both numbers are equal. k is a constant greater than 1. The simplicity of the rules stimulates the curiosity of the the orist. Admittedly, Silverman games do not seem to have a direct applied significance, but nevertheless much can be learnt from their study. This book succeeds to give an almost complete overview over the structure of optimal strategies and it reveals a surprising wealth of interesting detail. A field like game theory does not only need research on broad questions and fundamental issues, but also specialized work on re stricted topics. Even if not many readers are interested in the subject matter, those who are will appreciate this monograph.

This volume aims to present the basic results in the theory of two-person zero-sum repeated games including stochastic games and repeated games with incomplete information. It is intended for graduate students with no previous knowledge of the field.