an introduction to game theory and the law

T C L S

The Coase Lecture series, established in honor of Ronald H.Coase, Clifton R. Musser Professor Emeritus of Economics atthe University of Chicago Law School, is intended to providelaw students and others with an introduction to importanttechniques and results in law and economics. The lectures pre-suppose no background in the subject.

An Introduction to Game Theory and the Law

Randal C. Picker *‥

I am pleased to have the opportunity to give the third of thethree lectures in the Law School’s inaugural Coase Lecture Series. Ihave to confess I am still at a stage in life when I think about howthings will look on my resume, and to put down the Coase Lecture,I suspect, adds real luster to it. Nonetheless, we might want to callthese lectures something else. My suggestion is “The Bar StoolLecture Series.” That wouldn’t sound as distinguished and hencewouldn’t do much for my resume, but it more accurately captureswhat the mission of the talk is. Here is the test for this talk: Giventwo bar stools and a stack of cocktail napkins, could the ideas in thistalk be explained to an intelligent person in a crowded bar with abank of TVs showing the Bulls and the Blackhawks? If this talksucceeds at that level, I will have accomplished my mission; if it doesnot, then I will have to consult with the Dean to get a larger budgetfor eld research for my next big talk.

The bar stool test is a test of simplicity, of making an idea acces-sible to someone who is not a specialist in an area. It is a test that allof Ronald Coase’s work that I know passes quite easily. It is the re-markable combination of simplicity and depth, which I guess traveltogether if you are smart enough, that defines Coase’s work. Thematerial that I will discuss today is, I think, fairly simple, thoughsome of it is relatively new. And to give credit where credit is due,some of the work I will describe today is part of a joint effort withDoug Baird and Rob Gertner.

This will be an eight-cocktail-napkin talk: I want to talk abouttwo basic forms for games, the normal form and the extensive form;four ways of predicting the outcomes of games, through dominancearguments, Nash arguments, backwards induction, and forward in-duction; and two interesting ideas about game theory and the law.*Randal C. Picker is Professor of Law, University of Chicago LawSchool. I have benefited from extensive discussions with Douglas G. Bairdand Robert H. Gertner. I thank the Sarah Scaife Foundation and the Lyndeand Harry Bradley Foundation for their generous research support.‥

C W P L E . Game Theory and Strategic Behavior

As a discipline, law and economics advanced on the strong backof classical microeconomics. Individual decisionmakers maximizedutility or profits subject to constraints. These individuals were treatedeither as pricetakers in competitive settings or pricesetters in mo-nopolies. They were also perfectly informed. A sizable and largelysuccessful academic legal literature grew out of taking first derivativesand ruthlessly applying the discipline of the microeconomist’smarginal analysis to a vast array of legal problems.

The last twenty years have seen a major shift in the fundamentalmethodological tools used by microeconomic theorists. Game theoryhas emerged to augment the standard, polar approaches of purecompetition and monopoly. In a competitive setting, individuals orfirms are seen as having no real decisions to make. Prices are given,and individuals and firms are pricetakers. The other productionparadigm, monopoly, treats the monopolist as a pricesetter for agiven demand curve. In a game-theoretic setting, rational actorsneed worry about the actions of others—this is the fundamentalstrategic interdependence that game theory addresses. Other settingslack the back-and-forth quality that characterizes strategic settings.Game theory sounds like fun—visions of the gamut fromCandyland to Monopoly spring to mind. A definition might beuseful; as a rough cut, try: game theory is a set of tools and a languagefor describing and predicting strategic behavior. I will discuss in a bitwhat these tools are and how to apply them, but I want to focusfirst on the core concept in the definition, strategic behavior.Strategic settings are situations in which one person would like totake into account how a second person will behave in making a de-cision, and the second person would like to do likewise. Strategicsettings typically involve two or more decisionmakers, and the pos-sibility of linking one decision to a second decision, and vice versa. A sample of well-known textbooks and research monographs makes thepoint. Look at Mitch Polinsky’s Introduction to Law and Economics, which isnow in its second edition; Cooter and Ulen’s Law and Economics textbook,which came out in ; and two torts monographs, Landes and Posner’s TheEconomic Structure of Tort Law and Steven Shavell’s Economic Analysis of AccidentLaw, both of which were published in .

A I G T L Consider the airlines industry. Whether Northwest will cut faresmay depend on how American and United will respond, and thesame, of course, is true for them. Indeed, Northwest recently filedsuit against American, claiming that American’s introduction of anew pricing schedule was part of a scheme of predatory pricing de-signed to put Northwest out of business. Oligopolisticindustries—airlines, computer microprocessors or operating systems,for example—are natural settings for strategic interactions.

But so is a country road. I have risen for an early-morning walk.I would like to enjoy the view, take in the scenery, and generally ig-nore the cars going by me. You unfortunately are driving your newMazda Miata. You want to see how the car handles, to test how itdrives through turns and its acceleration. If I knew that you weredriving like a maniac, I would want to take that into account in de-ciding whether to pay much attention to the road. If you knew thatI was soaking in the countryside and ignoring the road, you wouldwant to take that into account as well. Our behavioral decisions areintertwined, and we need to take that fact into account when weseek to predict likely outcomes. The legal system should take thisinto account as well when it establishes antitrust laws for oligopolis-tic industries or a torts scheme for ordinary accidents.

. Normal Form Games, Dominant Strategies, and the Hidden Role ofLaw

. The Prisoner’s Dilemma

The best known bit of game theory is the Prisoner’s Dilemma. Iwill go through the analysis to make clear how much game theoryhas already crossed over and to establish some terminology, and willthen move on to more natural settings. So consider the following“game”: See Bridget O’Brian, “Predatory Pricing Issue is Due to be Taken Up inAmerican Air’s Trial,” Wall Street Journal, July , , .