Modeling Bounded Rationality.

By Ariel Rubinstein. Cambridge, MA: The MIT Press, 1998. Pp. viii, 208. $16.95.

The phrase "bounded rationality" is a Rorschach inkblot for economists. To some, including Herbert Simon, who originated the phrase, it is an empirical challenge to study the processes by which actual people make choices and learn from their mistakes. To other economists, bounded rationality is an opportunity to put aside standard formal models in favor of complex computational models or simple verbal models or no models at all. But to Ariel Rubinstein, bounded rationality is an opportunity to explore the formal models more deeply and to uncover strange and wonderful conclusions that follow from tweaking a few of the less realistic standard assumptions.

Rubinstein begins his slim and elegant monograph Modeling Bounded Rationality by explaining its scope and purpose. The book started as class notes for a specialized Ph.D. class and took shape in his 1996 Zeuthen lectures at the University of Copenhagen. Rubinstein excludes the related topics of evolutionary economics and learning and mentions empirical work only as an occasional motivation. The formal models he presents are not intended as definitive replacements for standard models but rather as attractive and thought-provoking samples of what can happen when strong rationality assumptions are relaxed.

Most chapters begin by pointing to a standard rationality assumption that seems problematic. What if a person doesn't have an established preference relation over the set of available alternatives but rather tries to simplify the choices (Chapter 2)? What if a person has imperfect recall (Chapter 4) or blurred perceptions (Chapter 5)? The focus is on isolated individual choice in the first half of the book but then turns to strategic interaction: what if players can't backward induct perfectly (as in solving chess, in Chapter 7) or find it costly to implement complex strategies (Chapters 8-9)? The chapter typically reviews the standard model, presents one or two possible modifications, and works out their consequences in simple cases. Each chapter closes with a brief guide to the published literature and with a class assignment that includes additional readings and research topics as well as routine exercises.

A more or less random example will help convey the flavor. Chapter 7 introduces Luce's choice rule as an alternative to utility maximization: a person chooses action [a.sup.*] in A with probability v([a.sup.*])/[[Sigma].sub.A] v(a), where the value v is some given positive function perhaps (or perhaps not) related to expected utility. Utility maximization (EU max) is the limiting case that the values of expected utility maximizing choices [a.sup.*] are arbitrarily large relative to the values v(a) of other actions. In two pages, Rubinstein crisply presents the definition and the corresponding Nash-type equilibrium, mentions the limiting behavior (for EU max and also the opposite direction) in a simple 2 x 2 symmetric matrix game, and goes off in a different direction in the next subsection. At the end of the chapter, he cites three important recent papers that use the same basic equilibrium concept, offers an exercise involving a simple parametric family of value functions, asks the student to compare and contrast the treatments in the three cited papers, and challenges the student to find procedurally rational underpinnings for Luce's choice rule.

The reader will find similar brief and tantalizing introductions to perceptions (the simplest sort of neural network), to Kripke's propositional calculus, to Marschak-Radner team theory and its relation to games of imperfect recall, to Turing machines, and to a host of other ideas including Rubinstein's own famous concept of complexity in automata games. Despite occasional typos, these brief introductions are notable for their clarity and attention to detail. For example, in his sketch of the folk theorem for repeated games, Rubinstein points out that his construction only covers outcomes in the relevant convex hull with rational weights on the extreme points and tells the reader where to look up the more complicated construction for the other points (with some irrational weights).

Despite the lucid presentation, the reader eventually will notice that the boundedly rational models tend to be more complicated than the original unboundedly rational models. So how can people with such tightly bounded rationality be smart enough to deal with the complicated model? Rubinstein's suggested answer is that the bounds apply to ordinary routine, but the routines are selected very carefully (pp. 98 and 162). I personally am not convinced and think that a story involving learning or evolution of routines would be more plausible. But such stories are beyond the chosen scope of this book.

Rubinstein bravely includes a final chapter featuring a critique of the book by Herbert Simon and a response. Simon writes, "At the moment we don't need more models; we need evidence that will tell us which models are worth building and testing" (p. 190). Rubinstein's defense is not that of a scientist but rather a mathematician: "The models of economic theory are meant to establish 'linkages' between statements that appear in our daily thinking . . . analogous to models in mathematical logic."

To my taste, Simon has the stronger case. But Rubinstein's book will have served its purpose admirably if it persuades more economic theorists and aspiring theorists to its viewpoint. And that would indirectly serve Simon's purpose as well, because the crucial empirical work is more likely to succeed when it is informed by a broader range of theoretical models.

The book is largely self-contained and is accessible to many audiences. Its strongest appeal will be to theoretically minded Ph.D. students who recently have mastered standard microeconomics and game theory. I plan to try it as a secondary text in such courses. Rubinstein evidently has used the material as the core of an advanced theory course. Not the least, applied economists with a taste for theory might want to read it just out of curiosity.

Daniel Friedman University of California, Santa Cruz