Two-Person Game Theory

by Anatol Rapoport

"Game theory is an intellectual X-ray. It reveals the skeletal structure of those systems where decisions interact, and it reveals, therefore, the essential structure of both conflict and cooperation." — Kenneth Boulding
This fascinating and provocative book presents the fundamentals of two-person game theory, a mathematical approach to understanding human behavior and decision-making, Developed from analysis of games of strategy such as chess, checkers, and Go, game theory has dramatic applications to the entire realm of human events, from politics, economics, and war, to environmental issues, business, social relationships, and even "the game of love." Typically, game theory deals with decisions in conflict situations.
Written by a noted expert in the field, this clear, non-technical volume introduces the theory of games in a way which brings the essentials into focus and keeps them there. In addition to lucid discussions of such standard topics as utilities, strategy, the game tree, and the game matrix, dominating strategy and minimax, negotiated and nonnegotiable games, and solving the two-person zero-sum game, the author includes a discussion of gaming theory, an important link between abstract game theory and an experimentally oriented behavioral science. Specific applications to social science have not been stressed, but the methodological relations between game theory, decision theory, and social science are emphasized throughout.
Although game theory employs a mathematical approach to conflict resolution, the present volume avoids all but the minimum of mathematical notation. Moreover, the reader will find only the mathematics of high school algebra and of very elementary analytic geometry, except for an occasional derivative. The result is an accessible, easy-to-follow treatment that will be welcomed by mathematicians and non-mathematicians alike.

Genres: Mathematics, Nonfiction

240 pages, Paperback

First published January 1, 1966

Reviews

[Vladivostok · Rating 2 out of 5]

Applicable in constrained scenarios with time-invariant rules. When and where is this useful outside of incredibly simple games?

[Greg · Rating 3 out of 5]

This is a very dated book on game theory, but it does have the advantage of being easy to understand and provides some crucial algorithms for solving two-person games, both zero-sum, and mixed strategy games. It covers games against nature as well. It also has the advantage of being very short. I recommend this book over Game Theory: A Very Short Introduction as a basic short introductory text for non-mathematicians, like business majors and political science majors.

[Creighton · Rating 5 out of 5]

This whole book is amazing! This book helped me understand game theory so well, and I couldn't have completed my senior undergrad projects without this resource. It's so readable! And, he explains everything so clearly that anyone can access this level of book. Even those who don't study math can understand completely! 10/10 recommend

[Jose · Rating 5 out of 5]

This book, although slim, is more of a textbook for an introductory course on game theory. It is by no means a brief read, but it has been simplified as much as possible for the layman to read.
I successfully struggled through in the first chapters, tripped up around chapter 8, and continued to be tossed around more and more into oblivion until the end of chapter 11 (chapter 12 is just concluding thoughts on the whole matter). I resorted to Googling and watching Youtube videos for extra instruction and elaboration.
At times it seems that this book gives more than you can chew to make sure that you at least get all the flavors before you decide to spit it out.
Otherwise, this book was very well written for its purpose; I like a challenging book and this did not dissappoint.
Those that are philosophically inclined will deeply appreciate this book; you will begin to see how zero-sum games, negotiations, saddle points, and insights from the prisoner's dilemma apply in real life; those that are not philosophically inclined will simply see an endless and pointless analysis of the interaction between two caricatures... those with no opinion can read chapter 12.

[Jolene · Rating 4 out of 5]

To be clear, I've only worked through Chs. 1-7 which give a good overview of 2 pp ZSG and (prudent) solution methods (an extension over the history of field--read previously). Good definitions and worked out examples. Much easier to go through discrete/numerical Castor-Pollux in pure prudent strat/minmax solution than extension to (variable version for) mixed strategy solution.

[Devin · Rating 2 out of 5]

Pretty interesting overall. He inserts a lot of his own opinion vaguely disguised as fact, which is slightly odd, but overall pretty informative.