Game Theory and the Law.

• Author: Salant, Stephen W.

With the advent of imperfect competition theory in the 1930s there appeared a profusion of oligopoly theories derived from a host of plausible assumptions, few of them readily testable by empirical evidence. It sometimes seemed as if every theorist aimed to produce a model of his own before breakfast each morning, limbering up with mental calisthenics.

No wonder that distinguished reviewers such as Leonid Hurwicz and Richard Stone eagerly welcomed the appearance in 1944 of von Neumann and Morgenstern's great work, The Theory of Games and Economic Behaviour. At last economists were properly equipped with powerful and elegant methods of tackling a subject that had become increasingly baroque . . . .

Surprisingly and embarrassingly and for reasons hard to fathom, over the next twenty years game theory failed to live up to its promise for economics. . . . [E]ven though as early as 1950 Nash had developed an appealing concept of solution for non-cooperative games, economists still shied away from applying game theory to strategic economic behaviour, its natural home in our discipline. . . .

[T]he analysis of strategic behaviour . . . languished mightily until the mid-1960s, when important papers by Harsanyi and by Selten and others appeared. By the 1970s this trickle of articles had become a swiftly moving stream, and by the 1980s a roaring flood that threatened to engulf the rest of microeconomics . . . .(1)

INTRODUCTION

The foundations of noncooperative game theory, the formal study of nonconsensual (or "strategic") interaction among self-interested rational actors, were laid largely during the middle of this century.(2) Since then, game-theoretic work has threatened to engulf not only microeconomics, but virtually every branch of social scientific study. The law rests on slightly higher ground, but certainly is not above the crest. The use of game-theoretic methods to study legal problems dates at least to the early 1970s,(3) and has been growing -- albeit at a more measured pace than in economics proper -- ever since. Almost surely, the differential rate of diffusion of game theory into law is due partly to its higher entry fee.(4) It has only been with increased numbers of individuals formally trained in both law and economics, as well as increased lawyer/economist collaboration, that game-theoretic analysis of legal problems has started to take off.

So it is only possibly surprising that Game Theory and the Law (hereinafter GTL) marks the first general effort to bring game-theoretic insights to a specifically legal audience. Even so, GTL might well encounter differing expectations among different segments of its potential audience. Some aspects of law and economics, in some quarters at least, are viewed as resting on undue simplification, whether in such forms as the core insight of The Problem of Social Cost,(5) or simply the relentless application to legal problems of the relentlessly economic weltanschauung of such economists as Gary Becker.(6) To be sure, the insights brought to bear on legal problems have been distinguished economic insights, and they have richly illuminated our thinking about the law. But it hardly requires citation to say that their application has often been controversial.(7) So, we conjecture at the outset, there are those who will approach both game theory generally and GTL particularly in a skeptical frame of mind, vigilant for the possibility that this may constitute an instance of cutting perhaps too wide a swath through the law with perhaps too simple, or too simplified, an economic thought.

We are happy to begin by reporting, then, that such apprehensions are without foundation. GTL decidedly does not bring to the law a single bright punch-line, distilled from a more ambiguous economic account. In part that is in the nature of the beast. But it also reflects the authors' aspirations, to which they can speak best themselves:

First, we wanted to introduce the formal tools of modern game theory to a wide audience using a number of classic legal problems . . . . Second, and as important, we wanted to show how modern game theory allows us to sharpen our intuitions and provides us with new ways of looking at familiar problems. In short, we have tried to write a book that offers those interested in law a new way of thinking about legal rules, and a book that shows those interested in game theory a fertile and largely unexplored domain in which its tools have many applications.

Much of the analysis in this book makes extensive use of concepts that have been developed only within the last decade, and we have not compromised on the rigor that these cutting-edge concepts demand. Nevertheless, we have been able to apply these concepts to the law without requiring the reader to know calculus, probability theory, or any other formal mathematical tools beyond simple algebra . . . . We depend only on the reader's willingness to think through hard problems logically and carefully. [pp. xi-xii].

This suggests that GTL will not be found erring on the side of undue or convenient simplification. Indeed that is the case. This is a broad foray, largely unburdened by doctrinaire predispositions, not only into the range of techniques deployed in contemporary game-theoretic work, but across the spectrum of law-related problems to which such techniques, in principle, can be applied.

The authors' prefatory observations nicely frame the issues on which we wish to dwell. Those are, first, how well chosen are their aspirations, and second, how well realized are the chosen aspirations? Given our venue, we take them up with a readership of lawyers curious about game theory -- rather than the other way around -- in mind. We will, however, say at the beginning, that, for the other segment of GTL's target audience -- game theorists interested in applications of their tools to the law -- this will be a very interesting book indeed, one that may well suggest a range of interesting topics on which to work. As for potentially interested lawyers, we imagine that they fall into one of roughly two groups: those already familiar with game theory, including those who do game-theoretic work themselves; and those with just a passing acquaintance, perhaps enough to understand the prisoner's dilemma and its moral, or possibly no more than enough to know that "strategic interaction" is a term that with increasing frequency they have heard. We assume that we can be of service primarily to the latter group, since those already conversant with game theory and the associated legal literature will be familiar with much of what is developed in GTL.

For readers interested in learning a little, or a little more, about both game theory and its relevance to the law, what might constitute a reasonable set of preliminary questions? Essential elements would seem clearly to include an introduction to what game theory is, an introduction to its principal analytic methods and illustrations of how they can be deployed to illuminate aspects of the law. GTL aspires to all of this and more. It introduces the reader to the more elementary game-theoretic techniques.(8) Most conspicuously, it surveys the ways in which the tools of game theory and information economics can be applied to aspects of the law. The survey takes in a lot of ground. It extends not only to advanced applications of game theory and information economics, but to such related topics as optimal contracting (pp. 109-18), mechanism design (Chapter Six), and bargaining (Chapters Seven and Eight). Unavoidably, then, it must introduce the reader to more-advanced techniques, and that is a third important feature of the book.(9) Finally, reflecting its multiplicity of authors and their current research interests, GTL incorporates detailed treatment of problems on which they separately have worked.(10) By any standard the undertaking is ambitious. It is also overdue. Game-theoretic work currently is scattered throughout the literature, at varying levels of accessibility and technical detail. There is a need for a general introduction to these materials.

At the extremes, the organizing thread of GTL -- its survey of applications -- could be spun out in one of two quite different ways. At each stage it could describe for the reader the techniques that were involved, and then proceed to articulate, above the level of gritty technical detail, how those techniques might be applied in particular legal settings, and with what insights and implications -- relegating the details to footnotes, appendices, or references to other texts.(11) This facilitates covering a lot of ground. Alternatively, it could take the time genuinely to school the reader in game-theoretic methods, developing the survey as a set of "worked-out" applications.(12) That would require a heavier investment by the reader and almost surely would limit the range of things surveyed. For the additional investment, however, the reader would end up with a better grasp of what actually is going on. With the former, the reader is more likely to end up with a sense of the insights that others have obtained by applying the techniques of game theory to the law. Either could produce a very useful book, although they would be very different books.

In important respects, GTL pursues the former course. It does not, as the preface immediately makes clear, require the reader to know -- or to learn -- any calculus (there is very little and, really, very little need) (pp. 112-16 & nn.34-38) or probability (of which there is a lot, none even remotely "theoretical," almost all of it as elementary as can be) (e.g., pp. 244-67 & nn.6-29). It does, by and large, develop its account of both the theory and its applications almost entirely in words. Those constraints effectively foreclose GTL from offering a genuinely systematic account of the range of game-theoretic techniques. Nevertheless, GTL does repeatedly expose the reader to...