This book departs from a very good set of questions: How can it be that several different behavioral sciences - sociology, social psychology, economics, biology - all study human social behavior, yet have vastly different conceptual frameworks? And perhaps more importantly: is there a way to unify these frameworks?
Professor Herbert Gintis is uniquely qualified to tackle these questions: as any reader of his Amazon book reviews can see, he is very widely read in all the social sciences, and much of his own research is interdisciplinary. Gintis proposes that game theory - a mathematical framework for analyzing strategic interactions between individuals - can play the role of unifying framework for the social sciences. The first half of the book is dedicated to explaining the basic concepts of game theory, and how it applies to basic issues in human social behavior.
The second half of the book is dedicated to connecting game theory to the sociological concept of a social norm. A central point in Gintis' argument is the concept of correlated equilibrium. A correlated equilibrium augments the well-known Nash equilibrium by adding a correlating device. A correlating device - or choreographer as Gintis' calls it - essentially is a random variable with the distribution over the set of strategy profiles. The correlating device selects a strategy profile (one strategy for each player) and tells each player what to do according to this strategy profile. If it is optimal for each player to follow the advice of the choreographer given her beliefs about what the choreographer advised the other players, a correlating equilibrium exist. As an example of this one can think of a traffic light. When the traffic light tells you to drive, it is optimal to do so, because you know the traffic light simultaneously tells other people to hold still. Thus, the traffic light coordinates the actions on the intersection.
Gintis maintains that the correlating equilibrium is a better candidate to provide the technical underpinnings of the concept of a social norm than the Nash equilibrium. Gintis argues that the social norm functions as a correlating device, which assigns a particular action to everyone engaged in interaction. Actions are in equilibrium when it is in everybodies' interest to follow the social norm if they expect others to do so. The reason that the correlated equilibrium is more suited to describe a social norm than the Nash equilibrium lies in the conditions that underly both concepts. While the Nash equilibrium relies on the assumption that all players in the game have correct expectations about the actions of all the other players, the correlated equilibrium merely requires that people share a common prior belief about the actions recommended by the correlating device. If the correlating device is a social norm, these prior beliefs are induced by indicators that activate the social norm. How such prior belief can come to be shared is the subject of an entire chapter.
Professor Gintis should be praised for his commitment to methodological unification. Especially worthwhile in this respect is the last chapter, where he proposes several concepts that could form the shared theoretical background in all the social sciences. He also submits some sensible proposals, such as the use of the correlating equilibrium, and the comments on methodological individualism are provoking and stimulating.
However, for several reasons I fear that the book will have limited influence in actually bringing together scientific disciplines. First, its organization is at times mysterious, and never argued for. The connections between the chapters are often unclear. There are some parts that will not interest most readers, like the extensive treatment of certain paradoxes in epistemic game theory. This relates to the second problem: the book is rather technical in its exposition. This will make it hard for anyone who is not steeped in mathematics or does not already know game theory. And anyone who has taken the trouble to learn game theory up to the technical level that is required to read Gintis' book will probably be already convinced of its usefulness. Third, the book is lacking in good examples. Although the argument surrounding the correlated equilibrium is connected loosely to a story about flagging taxis, this raises more questions than it answers. For someone who want to convince sociologists that game theory can be connected to basic sociological ideas like norm following and role theories, this is a rather serious omission. Finally, there are some harsh dismissals of alternative methodologies in the social sciences which, although I tend to find them reasonable, are bound to bruise some egos. Altogether, it is hard to escape the impression that this is a book for game theorists, by a game theorist, which is puzzling given its stated aim.
In short, a stimulating and impressive book with sensible ideas. Unfortunately, I fear it lacks the didactic sensitivity to reach across scientific disciplines, and thereby does not quite fulfill its lofty aim.