Game Theory and the Law: Baird, Gertner and Picker




This book rests on the premise that game theory can offer insights to those who want to understand how laws affect the way people behave. Laws often matter in situations in which the behavior of one person turns on what that person expects others to do. Because strategic behavior is common, the formal tools that can help us understand it are important. We set out to accomplish two goals in writing this book. First, we wanted to introduce the formal tools of modern game theory to a wide audience using a number of classic legal problems ranging from tort and contract law to labor law, environmental regulations, and antitrust. These problems are familiar to those who are trained in the law and readily accessible to those who are not. 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. Indeed, algebra is used only in a few places. In this respect, this book stands apart from other books that explore recent developments in game theory. We depend only on the reader's willingness to think through hard problems logically and carefully.

This book is the first to address in general terms the use of the formal tools of game theory and information economics in legal analysis and many of the models and ideas it sets out are new. Nevertheless, legal scholars have worried about strategic behavior for a long time and we have drawn on their insights. Moreover, there are many papers that take advantage of these tools in studying specific legal problems in subjects as diverse as procedure, contracts, conflicts of law, bankruptcy, taxation, and corporations. We have benefited from them as well. We also have relied heavily on work in law and economics and in game theory proper. The bibliographic notes at the end of each chapter give a sense of both the breadth of this literature and the connections between it and the ideas set out in each chapter. Given the extent of the literature, however, these notes are necessarily incomplete. There is a bibliography at the end of the book, as well as a glossary that defines the basic legal and economic terms that we use in the text.

We want to thank the many who have helped us on this project. The research support of the Lynde and Harry Bradley Foundation, the John M. Olin Foundation, the Sarah Scaife Foundation, and the Graduate School of Business at the University of Chicago made this book possible. We received many useful comments in workshops at George Mason University, New York University, the University of Pennsylvania, and the University of Virginia.

In-Koo Cho, Cass Sunstein, and Alan Sykes gave us valuable advice throughout the project. Patrick Bolton, Richard Epstein, Frank Easterbrook, David Friedman, and Mitchell Polinsky gave us the benefit of their close reading of several chapters. We are especially grateful to Ian Ayres, Jon Elster, Daniel Farber, Mark Fisher, Ted Frank, William Landes, Richard Posner, Mark Ramseyer, Robert Rasmussen, Eun Shin, David Skeel, and Lars Stole for extensive written comments on the entire manuscript.






Understanding Strategic Behavior

Strategic behavior arises when two or more individuals interact and each individual's decision turns on what that individual expects the others to do. Legal scholars have long recognized the need to take account of strategic behavior. Too often, however, they have not taken advantage of the formal tools of game theory to analyze strategic behavior other than to invoke such simple games as the prisoner's dilemma as a metaphor for a collective action problem. This alone may not help us much. It may not matter much whether we call something a collective action problem or a multi-person prisoner's dilemma. This failure to make better use of game theory is unfortunate. Modern game theory is sufficiently powerful to offer us insights into how legal rules affect the way people behave. The challenge is one of applying its highly technical tools, many of which have been developed only in the last decade, to a new environment.

We begin in the first chapter with a problem-the tort rules governing an accident involving a motorist and a pedestrian-that is already well understood. Our ambition is to show how even in the context of so simple a problem, a rigorous focus on strategic behavior advances our understanding of the legal rules. In the second part of the chapter, we review the best known paradigms of game theory, such as the stag hunt, the prisoner's dilemma, and matching pennies, and show both how they may be applied to legal problems and what limits we encounter in doing this. Chapter 2 examines how parties interact with each other over time. We use the problem of market preemption in antitrust law and several issues in debtor-creditor and contract law as vehicles for introducing additional game-theoretic tools.

Subsequent chapters explore more difficult issues. Incomplete information is the central problem in game theory and the law. Shaping laws that give parties an incentive to act in a way that leaves everyone better off is a straightforward matter as long as all the parties and those who craft and enforce the legal rule all possess enough information. Complications arise, however, because the necessary information is often not known or, more commonly, is known, but not to all the parties or not to the court.

Chapter 3 focuses on the simplest information problem. With respect to some kinds of information, legal rules have to confront a problem of unraveling, situations in which the ability of people to draw inferences from silence leads to the revelation of information. With respect to other kinds of information, we have to focus on the problems of signaling and screening, the ability of parties to draw inferences from the actions that parties take. In both cases, we have to take account of the ability both of other parties to acquire information and of a court to acquire it. These distinctions should guide our understanding of such questions as legal rules governing the renegotiation of contracts. We develop a new model that shows how legal rules affect contracts that are written with the possibility in mind that the parties may want to renegotiate its terms at a later time.

We go on in Chapter 4 to analyze legal rules that must work in situations in which in which one party possesses information that cannot be communicated credibly to other parties or a court. Inferences about the information must be drawn from actions that the parties take. Advances in game theory now provide a rigorous way to explore how changes in legal rules affect the ability of parties to draw such inferences. Various legal regimes, such as plant closing laws and the Americans With Disabilities Act, can be put in this framework and subjected to scrutiny.

Chapter 5 examines how legal rules may affect parties who interact with each other over time. We illustrate this problem first by examining the Statute of Frauds, the contract law principle that requires most contracts to be evidenced by a writing. We show how a new way of interpreting the Statute of Frauds emerges once the problem is seen as a repeated game. We then examine a number of problems in antitrust law, including tacit collusion and predatory pricing. We use these problems as a vehicle for showing how legal rules affect the ability of parties to develop reputations that lead not only to anti-competitive conduct, but also to long-term cooperation.

Chapter 6 examines a number of different collective action problems. It shows the dangers of examining interactions between parties and treating them as stand-alone games rather than as part of a larger game in which they are embedded. Legal rules often treat collective action problems when information is incomplete. We show how the mechanism design literature allows us to set out the limits of what legal rules can do in these situations. The chapter also explores network externalities and herd behavior and the subtle ways in which the actions of one individual can impose costs on others.

How parties bargain with each other and the way in which they split the surplus from trade between them is a problem that recurs in legal analysis. Noncooperative bargaining theory provides a vehicle for understanding the dynamics of negotiations. In Chapter 7, we first examine an important question of contract law involving the availability of specific performance when the loss a party suffers from breach is private information. We show how the problem can be seen as a bargaining game in which there is private, nonverifiable information and we show how this game can be solved. This model, like many others we develop in the book, is new. When applied to bankruptcy law, the same model suggests unappreciated strengths and weaknesses of the automatic stay and the new value exception to the absolute priority rule in bankruptcy, and several labor law doctrines, including limits on the ability to hire permanent replacements.

In Chapter 8, we focus again on the dynamics of bargaining and in particular on the way in which legal rules governing bargaining must take account of the possibility that one or both of the parties may possess private information. We use a number of examples from the rules governing civil procedure to illustrate these problems. We incorporate two-sided private information into the standard model of bifurcated trials and we create a new model to explore rules governing discovery, a problem that by its nature turns on private information. In addition, we show that private information is likely to have important effects on the kinds of cases that are litigated and the inferences one can draw about the law from reported decisions.

Although we touch on many different legal problems in the course of the book and draw on much of the work that has been done in noncooperative game theory and information economics, particularly in the last decade, we also show that only a few basic paradigms are needed to capture the essential problems of strategic behavior that legal rules need to take into account. It is with the simplest paradigm-that of simultaneous decisionmaking under complete information-that we begin the first chapter.

Bibliographic Notes

The Problem of Strategic Behavior. John von Neumann is generally recognized as the founder of modern game theory. Von Neumann (1928) and Von Neumann and Morgenstern (1944) are the two important early works. John Nash also made seminal contributions to game theory. See Nash (1950a) and Nash (1950b). Schelling (1960) is a classic nontechnical introduction to game theory as well as one of the first works to enlarge significantly the scope of game theoretic issues in the political and social sciences. A number of excellent introductions to game theory now exist. The best formal introductions to game theory include Fudenberg and Tirole (1991a), Kreps (1990b), and Myerson (1991). Fudenberg and Tirole (1991a) is encyclopedic and is a useful reference for understanding many game theoretic concepts. Kreps (1990b) connects the tools of game theory to the foundations of microeconomics. Hirshleifer and Riley (1992) is a good formal introduction to information economics.

Several excellent books on game theory aimed at nonspecialists have also been published in recent years. These include Binmore (1992), Dixit and Nalebuff (1991), Gibbons (1992), Kreps (1990a), and Rasmusen (1989). Both Binmore (1992) and Gibbons (1992) are formal introductions to game theory that are accessible to nonexperts. Gibbons (1992) focuses especially on applications of game theory to many standard economic problems. Rasmusen (1989) takes as its central focus the role of information. These books, however, require readers to be familiar with single-variable calculus and basic probability theory.

Dixit and Nalebuff (1991) is a nontechnical book that illustrates the general ideas of game theory using examples drawn from sports, business, and other familiar contexts. Kreps (1990a) discusses game theory and the conceptual underpinnings of its solution concepts.

Game Theory and the Law. The early applications of economic reasoning to the law were done with an eye towards understanding how legal rules affect behavior. The more prominent of these seminal works include Coase (1960) and Calabresi (1970). Posner (1992) offers a comprehensive examination of the economic analysis of law. First published in 1973, it remains the starting place for analyzing many of the questions whose strategic components are the focus of this book. Farber and Frickey (19) show how public choice theory can illuminate legal analysis. See also Coase (1988) and Buchanan (1989) for more detail on Coase and the combination of legal issues and economic logic.

The amount of legal scholarship that uses game theory in analyzing particular legal problems is large and growing. For example, Ayres (1990) provides a general discussion. Jackson (1982) applies the prisoner's dilemma to bankruptcy law. Cooter, Marks, and Mnookin (1982) is one of the first to use an explicit game theoretic model to examine what takes place before trial. Bebchuk (1984) and Bebchuk (1993) use information economics and game theory to examine rules of civil procedure. Mnookin and Kornhauser (1979) and Mnookin and Wilson (1989) examine strategic bargaining in the context of family law and bankruptcy respectively. Katz (1990) use game theory to analyze the problem of offer and acceptance in the law of contracts. Johnston (1990) uses game theory to explore contract default rules. Gordon (1991) and Leebron (1991) use it to look at corporate law. Menell (1987) draws on the network externalities literature to analyze copyright protection for computer software. Brilmayer (1991) employs game theory to analyze problems in the conflicts of laws, as does Kramer (1990). Ellickson (1991) uses game theory in a number of places to show how custom can work in much the same way as legal rules.

Copyright 1995-2000, Randal C. Picker