Introduction to the Theory of Games

by J.C.C. McKinsey

Book Overview

One of the classic early monographs on game theory, this comprehensive overview illustrates the theory's applications to situations involving conflicts of interest, including economic, social,... This description may be from another edition of this product.

• Format: Hardcover
• Language: English
• ISBN: B009D9ZT6O
• Release Date: January 1952
• Publisher: McGraw-Hill
• Length: 371 Pages
• Weight: 2.10 lbs.

Customer Reviews

Thorough theoretical description of the concept of the "game"

The inclusion of the word "introduction" in the title does not mean elementary, the level of mathematics is very advanced. In the broadest definition of the term, "game" it is a set of optional choices where the goal of the selectors is to maximize or minimize their return, often relative to an opponent. That is the definition used in this book. Few actual games are mentioned and many theorems and proofs are included. The chapter titles are: *) Rectangular games *) The fundamental theorem for rectangular games *) The solutions of a rectangular game *) A method of approximating the value of a game *) Games in extensive form *) Games in extensive form - general theory *) Games with infinitely many strategies *) Distribution functions *) Stieltjes integrals *) The fundamental theorem for continuous games *) Separable games *) Games with convex payoff functions *) Applications to statistical inference *) Linear programming *) Zero-sum n-person games *) Solutions of n-person games *) Games without zero-sum restriction: the vonNeumann-Morgenstern theory *) Some open problems To understand the material in this book, you need a solid grounding in differentiable and integral calculus, linear algebra, probability and stochastic processes. However, if you have that background, you will find an understandable and nearly complete theoretical description of the general concept of games.

An Early Masterpiece in Game Theory

I developed an interest in game theory some years ago and began collecting a small library of acknowledged "essential references" in the subject in order to educate myself. Of all the books that I own, this masterpiece by J. C. C. McKinsey stands out for its clarity of exposition, its amazingly clear logical organization, and its readability. Any sufficiently motivated person with the requisite mathematical background can teach himself a fair amount of game theory by studying this book on his own. McKinsey's book is a model of what mathematical exposition SHOULD be (but rarely is). The book appeared in 1952 and hence is hopelessly out of date; game theory has undergone significant development in the past few decades. However, McKinsey's book still offers the clearest introduction to the established "core" materials to be found in any text. In fact, I have repeatedly found that McKinsey's book, together with the old 1957 classic by Luce and Raiffa, provides novel insights and enlightening discussions that are not to be found in any of the most popular standard references currently in use in university-level game theory courses. In addition to his interests in game theory, McKinsey was a logician of some repute. It is our loss that he died under tragic circumstances in 1953 when merely 45 years old. His death came only one year after the release of his book on game theory and two years after his separation from the Rand Corporation, where so much of the early work in game theory took place. We can only speculate how this magnificent book might have evolved through successive editions had McKinsey lived another 30 years.