Publisher: Princeton University Press (2009)Details: 286 pages, Hardcover
Price: $35.00
ISBN: 9780691140520
Category: Monograph
Topics: Game Theory, Mathematical Economics, Mathematics for the Social Sciences
Herbert Gintis
Publisher: Princeton University Press (2009)
Details: 286 pages, Hardcover
Price: $35.00
ISBN: 9780691140520
Category: Monograph
Topics: Game Theory, Mathematical Economics, Mathematics for the Social Sciences
[Reviewed by William J. Satzer, on 05/28/2009]
Game theory, according to the author, is an indispensable tool for modeling human behavior. He believes that behavioral disciplines that reject game theory or regard it as peripheral are handicapped theoretically. (“Behavioral disciplines” here include psychology, economics, anthropology, sociology, political science and some aspects of biology.) At the same time, the author notes, many champions of game theory make extravagant claims about it; indeed, some think it capable of explaining all aspects of human social existence.
Throughout the book the author attempts to put game theory in perspective for the behavioral sciences. One of his main contributions here is to point out that the Nash equilibrium, the traditional equilibrium concept of game theory, is achieved by rational actors only when they share beliefs about how the game is to be played. He proposes instead the concept of a correlated equilibrium wherein the correlating devices can be broadly identified with social norms. The author contends that game theory in the social sciences needs a broader social theory behind it.
The author is an economist and an advocate of evolutionary game theory, which – he believes – can remedy many of the weaknesses of traditional game theory. His Game Theory Evolving is a companion volume to the book of this review. There is a fair amount of mathematics in the current book, and it ranges from the analysis of special games to axiom systems and a symbolic description of properties of a knowledge operator in modal logic. I did find the following comment from the author’s preface rather troubling:
"Game theory can be used very profitably by researchers who do not know or care about mathematical intricacies but rather treat mathematics as but one of many tools deployed in the search for truth. I assert then that my arguments are correct and logically argued. I will leave rigor to the mathematicians."
(Would the author claim similar infallibility for his non-mathematical arguments?) It is especially bothersome because there are enough typographical errors throughout the mathematical sections to make some of the author’s arguments incomprehensible. It is difficult even to make sense of some of the expressions because they are so scrambled. In other places, arguments are so abbreviated — and at times, unsupported — that they’re very hard to follow. Given that, I have to wonder what the mathematical portions of the book were meant to do, how they might serve its readers, and indeed just who the intended readers might be.
The strengths of the book are in the author’s command of the scope of game theory across the behavioral sciences and in his assessment of the needs for modifications to the way game theory is applied in those disciplines. The value of the book to a mathematical reader is that broad perspective of how game theory is applied in the behavioral sciences.
Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.