The book is based partly on earlier research by von Neumann, published in 1928 under the German title "Zur Theorie der Gesellschaftsspiele" (
"On the Theory of Board Games"). The derivation of
expected utility from its axioms appeared in an appendix to the Second Edition (1947). Von Neumann and Morgenstern used objective probabilities, supposing that all the agents had the same probability distribution, as a convenience. However, Neumann and Morgenstern mentioned that a theory of
subjective probability could be provided, and this task was completed by
Jimmie Savage in 1954 and
Johann Pfanzagl in 1967. Savage extended von Neumann and Morgenstern's axioms of rational preferences to endogenize probability and make it subjective. He then used
Bayes' theorem to update these subject probabilities in light of new information, thus linking rational choice and inference. The book begins with a preface. This is then followed by a chapter on the
Formulation of the Economic Problem and one on a
General Formal Description of Games of Strategy. Zero sum games are then introduced. Firstly with a chapter on a
Theory of Zero-Sum Two-Person Games, then one on
Examples, and then one on
Three-Person Games Zero Sum games. A
General Theory: Zero-Sum N-Person Games is offered and then a chapter on
Four-Person Zero-Sum games. After these is a chapter offering
Some Remarks Concerning N ≧ 5 Participants Games. Then chapters on the
Composition and Decomposition of Games, one on
Simple Games and one on
General Non-Zero-Sum Games are provided. The final chapter is on
Extensions of the Concepts of Domination and Solution. After this at the end of the book there is an appendix offering an
Axiomatic Treatment of Utility. == Reception ==