These lectures were presented to a group of upper division and graduate students at Princeton University in the spring term of 1952. They are intended as an introduction to the relatively modern mathematical discipline known as the Theory of Games. In an attempt to make them somewhat self-contained, considerable space has been devoted to topics which, while not strictly the subject matter of game theory, are firmly bound to it. Principally, these are taken from the geometry of convex sets and the theory of probability distributions. No previous knowledge of these subjects has been assumed; it is only supposed that the reader has an acquaintance with the calculus and with elementary matrix theory and vector analysis. References to tangential matters are given in notes appended to each chapter.
With a few exceptions, the text follows the lectures exactly as they were presented; the author is indebted to Mr. C. S. Coleman for keeping an accurate record of the content. There has been one deliberate and significant omission, namely, the theory of games with more than two participants. It was felt that this portion of the theory is in such a violent conceptual transition that it would require more time and space for an adequate synthesis than these lectures provided.
Valuable contributions have been made by a number of individuals. In particular, thanks are due to L. S. Shapley and I. Glicksberg for fruitful discussions of the presentation of various sections; to David Gale and A. W. Tucker, with whom the author has developed his attitudes toward the subject matter of game theory; to L. Hutchinson, who found a number of errors; and to Euthie Anthony, who did the painstaking work of typing the master copy of the original report of the Logistics Research Project.
Harold W. Kuhn
Bryn Mawr College