Vol. 5 No. 6 (June, 1995) pp. 179-182

GAME THEORY AND THE LAW by Douglas G. Baird, Robert H. Gertner and Randal C. Picker. Cambridge, Mass.: Harvard University Press. 330 pp. Cloth $45.00.

Reviewed by Jack Knight, Department of Political Science, Washington University in St. Louis

GAME THEORY AND THE LAW is an important book. It is important in the sense that it will serve as a catalyst for an expanded use of game-theoretic models in the study of law. It will be a book that people will one day recognize as having had a considerable influence on its field. And it will receive the praise that accompanies such influence. Happily, such influence will be beneficial to the field of law and such praise will be richly deserved, because GAME THEORY AND THE LAW is an extremely intelligent and thoughtful text. I recommend it without reservation to students of law and politics (and to those of law and economics, for that matter) and, more generally, to students of game theory and strategic behavior. Baird, Gertner and Picker set two goals for themselves in writing this book: (1) "to introduce the formal tools of modern game theory to a wide audience using a number of classical problems ranging from tort and contract law to labor law, environmental regulations, and antitrust" and (2) "to show how modern game theory allows us to sharpen our intuitions and provides us with new ways of looking at familiar problems." (p. xi) The authors achieve both of these goals and more in a very impressive fashion. Their sophisticated grasp of the intricacies of game theory as well as of the strategic dimensions of many areas of the law is manifest throughout the volume. Their analysis is analytically rigorous, but not mathematically complex. For those readers who are wary of mathematics for one reason or another, I can assure you that the authors are able to translate sophisticated and complex mathematical concepts into fairly simple ones without failing to communicate the underlying point of the concept.

More importantly, one of the features of the book that is most striking (and, for my part, most welcome) is the thoughtful and sensible manner in which they approach the use of game theory. Unlike many proponents of game-theoretic analysis, they do not present it as the only legitimate approach to social-scientific analysis. The authors present game theory as a powerful tool that can be used along with other approaches to enhance our understanding of the role of law in social life. They straightforwardly acknowledge what many take to be a criticism of game theory -- that game-theoretic models simplify the reality of social interactions -- but they assert quite rightly that such simplification is not a problem as long as we remain clear about why we are using the model: to compare the possible effects of different legal rules on those interactions. They suggest that "[t]he test of a model is whether it can hone our intuition by illuminating the basic forces that are at work but not plainly visible when we look at an actual case in all its detail." (p. 7) They also offer a reasonable response to another oft-cited criticism of game-theoretic analysis -- the assumption of maximizing self-interested behavior in writing:

The basic assumption at the heart of this mode of analysis is not that individuals are self-interested

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profit-maximizers or care only about money, but rather that they act in a way that is sensible for them given their own tastes and predilections. This assumption may not always hold in an individual case, because people at times act in ways that are inconsistent and self-destructive. In general, however, people make the best decisions they can, given their beliefs about what others will do. (p. 11)

They offer solid cautionary advice (especially in an extended discussion in chapter six) about the care necessary to avoid using the wrong models to analyze subtle social situations. (How many of us have wondered whether the world really is one big Prisoner's Dilemma game?) Finally, throughout their analysis they maintain a realistic view of the assumptions about the world to which we commit ourselves when we employ game-theoretic solution concepts, assumptions that may lead us to draw false inferences about the effects of legal rules on strategic behavior. In discussing the move from a less restrictive to a more restrictive solution concept, the authors note that "we must assume more about what individuals know and more about how they believe others will act. The more we have to make such assumptions, the less certain we can be that our model will accurately predict the way individuals behave." (p. 13)

Having set forth their understanding of the strengths and weaknesses of game-theoretic analysis in their early discussion, Baird, Gertner and Picker proceed in the course of the book to make a powerful case for the value of the approach. To give an adequate sense of the sheer breadth of their coverage, I will merely outline the issues -- both game-theoretic and legal -- that they address in their eight chapters. In the first chapter they present the basic assumptions of strategic behavior and introduce static games and their basic solution concepts (including Nash); they discuss tort laws governing negligence and the duty of due care. In the second chapter they incorporate time into the analysis and begin a consideration of extensive form games (including an exceptionally clear and informative explication of the subgame perfect solution concept); they demonstrate the relevance of models of ongoing interactions in the areas of antitrust law and debtor-creditor relations. In chapters three and four they introduce the complexity of incomplete information, the realistic assumption that there is important information relevant to the social interaction that is unknown to either one or both of the actors. The authors call incomplete information "the central problem in game theory and the law." (p. 2) From a strategic perspective they develop the issues of unraveling, signaling, screening, the crucial role of beliefs in games of incomplete information and the basic incomplete information solution concept, perfect Bayesian equilibrium, and some of its refinements; from a legal perspective the authors show how incomplete information influences the effect of legal rules in such areas as plant closing laws, parental leave provisions, disclosure laws, inquiry limits (including a provocative discussion of the

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Americans with Disabilities Act) and various laws that govern contracts that envision future renegotiations. In chapters five and six they consider a set of issues related to problems of collective action and cooperative behavior. The game theoretic issues included in these chapters include repeated games, the problem of multiple equilibria, the folk theorem, the effect of reputation and mechanism design; the legal issues include the Statute of Frauds and antitrust regulations governing predatory pricing and tacit collusion. In the last two chapters the authors introduce distributional considerations including an explication of non-cooperative bargaining theory (both the classic Rubenstein model and various models which incorporate assumptions of incomplete information); then they demonstrate the value of these models for understanding bankruptcy law (including the provisions governing automatic stays and the new value exception), labor law (restrictions on hiring permanent replacement workers) and rules of civil procedure (including provisions covering pre-trial discovery procedures and rules dictating the structure of hearings and trials.)

But even more than through their comprehensiveness, the authors' case for the value of game theory is made through the creativity of their analysis. To highlight this creativity, I will briefly discuss two examples of the significant insights which they offer. First, as I have previously stated, the problems related to information are, in the minds of the authors, fundamental to law. They emphasize the importance of the distinction between verifiable and nonverifiable information. Through their analysis of social interactions that are characterized by these different types of information, they demonstrate one of the major insights of their analysis: legal rules intended to affect the communication of private information (that is, information known to only some of the actors involved in an interaction) will have different effects depending on whether or not the information is verifiable (by either the other actors or a court.) An especially striking feature of this insight is captured in their claim "[t]o understand the effects of a legal rule, we must pay attention to the way it affects not only actions that the parties actually take, but also actions that they would not have taken even in the absence of a legal rule." (p. 156) Here the value of the use of game theory is most telling because this particular insight is explicitly derived from the implications of the game-theoretic concept of off-the - equilibrium path beliefs (basically, the idea that people are often affected in how they will act by their expectations of what those with whom they interact will do if they themselves were to act differently.) Through a set of legal examples analyzed by a simple model of incomplete information, the authors show that the law can influence behavior by establishing rules that prohibit behavior that the actors would not do even if the rule was not in place. For example, in a situation in which employers are known to discriminate against disabled job applicants, the authors find that the equilibrium outcome is that disabled applicants misrepresent their disabilities and thus employers treat all applicants similarly. When the authors introduce a rule that prohibits discrimination based on disability, the equilibrium outcome changes to one in which the disabled workers reveal their disabilities and the employer adopts a work plan that differs for disabled and nondisabled workers and which produces a superior

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outcome for both workers and the employer. Thus, a rule that prohibits an action that the employer would not even take if the actors were being strategically rational nonetheless produces a change in behavior that is socially optimal.

Second, the authors show how game-theoretic analysis can provide insights into how we might make mistakes in our analysis of the effects of legal rules. Their analysis shows that studies of the effects of discovery rules on civil litigation will misconstrue those effects if they focus merely on the cases that go to trial. The authors demonstrate a selection bias in such a study sample. By analyzing the strategic effects of discovery rules on pre-trial negotiations, the authors show that some discovery rules have the effect of causing those parties who are most likely to be liable to settle their cases before trial, thus selecting out those cases most likely to result in a judgment for the plaintiff. Because of this pre-trial effect, the cases that do actually go to trial are disproportionately those most likely to lead to a judgment for defendants (because people who know that they are not liable are the ones least likely to accept a settlement offer.) If analysts were to base their investigation of rules of civil procedure merely on the cases that go to trial and judgment, they would, on the authors' analysis, fail to capture important effects of these rules. This selection bias is clarified by the use of a simple game-theoretic model of litigation.

These are merely two examples from a wealth of insights offered by Baird, Gertner and Picker. The persuasiveness of their general argument for the utility of game theory derives from a combination of the power of their insights along with the sensibility of their analysis. The book is written in a clear, concise and interesting manner. Its bibliographic references render it a source book for additional research in both game theory and law. This is a book that should be read by scholars of law in particular and scholars of political behavior in general. One of the best compliments that I can give it is that it would also be a profitable investment for those who focus primarily on formal models of strategic behavior and games.

Copyright 1995