This remarkable publication is based on Harold Kuhn's lectures on the theory of games held in 1952 at the Princeton University. It was supposed to appear in the Annals of Mathematical Studies in 1953 but the author decided to extend the contents substantially and to postpone the publication. However, the intended extension for games of more than two persons did not take place and finally, with the delay of 50 years, Princeton University Press published the original text. As a whole, the book provides interesting and valuable author's insights on the theory of games, a new mathematical discipline developing rapidly a half a century ago. Matrix games are presented in Section 2 along with necessary results from convex analysis and an interesting survey of alternative proofs of the minimax theorem. The next Section is devoted to games in the extensive form and the last Section deals with the games on unit square and includes also basic concepts of measure theory and probability. The book contains many illuminating and motivating examples. Numerous exercises appear at well chosen places of the text to support reader's understanding.

Reviewer:

jdup