Law and economics cases and materials

Law and Economics
Cases and Materials
Charles J. Goetz
Hartfield Professor of Law

© Copyrights 1984-2006, All Rights Reserved


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Table of Contents

CH. 1: ANALYZING CHOICE UNDER ALTERNATIVE RULES

1

A.

INTRODUCTORY CONSIDERATIONS

1

B.

ELEMENTARY GAME THEORY

5

1.

THE PRISONER’S DILEMMA
THE STUDENT’S DILEMMA: UNIVERSITY v. EAGER
THE PRISONER’S DILEMMA AS A MATRIX MODEL
Exhibit 1.1: PD Matrix Model
c.
THE “PRISONER’S DILEMMA” DEFINED
Exhibit 1.1: PD Matrix Model

a.
b.

5
7
8
8
9
10

2.

ANOTHER IMPORTANT, CLOSELY RELATED GAME: “CHICKEN”

11

3.

OTHER USEFUL JARGON: “EXTERNALITIES”

11

4.

ETHICAL AND OTHER EXTRALEGAL BEHAVIORAL REGULATIONS

12

5.

EXTERNAL BENEFITS, EXCLUDABILITY AND “FREE RIDERS”

15

C.

THE LAW AND ECONOMICS OF PROPERTY RIGHTS

16

1.

ROAD MAINTENANCE PROBLEM
Exhibit 1.3 Benefits of Road Repair Levels

16
16

2.

JOINTNESS AND EXCLUDABILITY AS ELEMENTS OF PROPERTY

17

3.

CHICKEN vs. PRISONER’S DILEMMA
Exhibit 1.4 Road Problem As A “Chicken” Game
Exhibit 1.5 Road Problem As A Prisoner’s Dilemma

18
19
19

4.

GAMING ABOUT INFORMATION
UNTRUTHS CAN IMPROVE BUSINESS-SCHOOL GRADE; PEER PRESSURE CLASHES WITH
ETHICS

20

5.

“CHICKEN” IN ACTION: LAND ASSEMBLY
HOMEOWNER BICKERING ENDS $100,000 OFFER FOR HOUSES

22
22

6.

WHAT GENERALIZATIONS CAN BE MADE?

23

D.
1.

2.
d.

TRANSFERABILITY AS AN ELEMENT OF PROPERTY

20

23

ASSIGNABILITY OF CAUSES OF ACTION
THE CASE OF NIKE v. LOBEL

24
25

OTHER KINDS OF PROPERTY RIGHTS IN LEGAL PROCESS
Mutuality of Estoppel

27
27


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Goetz, Law and Economics

e.

3.

Discovery of Computerized Litigation Files
BROADCAST MUSIC, INC. v. MOOR-LAW, INC.

COASE AND COSTS, “OPPORTUNITY” AND OTHERWISE
Allocation of Rights in the Small-Number Context
FONTAINEBLEAU HOTEL CORP. v. FORTY-FIVE TWENTY-FIVE, INC.
b. Applicability of the Coase Theorem
c.
Cases Involving Transactions-Cost Problems
BOOMER v. ATLANTIC CEMENT CO.
Bomber v. Particular Gypsum Co.
J. WEINGARTEN, INC. v. NORTHGATE MALL, INC.
SPUR INDUSTRIES, INC. v. DEL E. WEBB DEVELOPMENT CO.
SPRECHER v. ADAMSON COMPANIES et al.
a.

28
28
30
31
31
32
35

35
37
37
40
43

CH 2: RIVALROUS AND RISKY DECISIONS

47

A.

47

BEHAVIOR INVOLVING UNCERTAINTY

1.

PROSPECTS AND CERTAINTY EQUIVALENTS

47

2.

EXPECTED VALUES
Exhibit 2.1 Computing Expected Values

48
48

3.

RISK PREFERENCE
Exhibit 2.2 Money and Utility

49
50

B.

APPLICATIONS

52

1.

LAW OF THE LEANING TREE

52

2.

THE CASE OF MRS. CRISPY’S CHICKEN

53

3.

EX ANTE ANALYSIS OF PUNISHMENTS
IN RE JOHN LYNCH

RICHARDS v. ALLSTATE INSURANCE CO.
CRAIG v. BOREN

54
54
58
60

4.

THE HUNTING OF A TAKEOVER

63

5.

AGENT-PRINCIPAL CONFLICTS OF INTEREST
Using Agents To Sell Real Estate
Exhibit 2.3 - Real Estate Market Information
b. Agent-Principal Conflicts in Legal Contracts
HEINZMAN v. FINE, FINE, LEGUM & FINE

a.

6.

“CURVE” MODELS: MARGINAL AND TOTAL EFFECTS
Exhibit 2.4 – Marginal Effect As Slope of Total Curve
Exhibit 2.5 - Area Under A Marginal Curve

65
65
65
67
67
69
70
70


Table of Contents

iii

7.

ATTORNEY- CLIENT RELATIONSHIPS

71

8.

SHOULD SUBROGEES KEEP “EXCESS” RECOVERIES?

72

C.

LEAST-COST RISK BEARING

73

1.

WHAT IS “LEAST-COST” RISK BEARING?
Exhibit 2.6 – Binomial Distribution

73
75

2.

SOURCES OF LEAST COST RISK-BEARING
Exhibit 2.7 – Pool of 5 Shared $1 Risks with 40% Probability
Exhibit 2.8 – Pool of 10 Shared $1 Risks with 40% Probability
Exhibit 2.9 – Pool of 20 Shared $1 Risks with 40% Probability

76
77
78
78

3.

PORTFOLIO ANALYSIS AND THE PRUDENCE STANDARD

79

D.

OPTIMAL INSURANCE AND RISK ADJUSTMENT

80

1.

“INSURANCE” AGAINST CONTRACT BREACH
Exhibit 2.10 (top panel) and Exhibit 2.11 (bottom panel)

80
82

2.

AFTER-THE-FACT INDEMNIFICATION: REALLY INSURANCE?

83

3.

“RISK DISTRIBUTION” INSURANCE AGAINST HARMFUL EVENTS
NATIONAL STEEL SERVICE CENTER v. GIBBONS

85
85

E.

JUSTICE AND FAIRNESS

88

1.

A Contractarian Theory of Justice as Fairness
Exhibit 2.12 – Social Choice Matrix
Exhibit 2.13 – Maxi-Min Social Choice Matrix

88
89
91

2.

FAIR DIVISION SCHEMES: DIVIDE AND CHOOSE

91

3.

EQUITABLE DISTRIBUTION OF VOTING POWER
Pivotal-Voter Measure of Political Power
Exhibit 2.14: Power of a Voter Via Representation
b. An Equilibrium-Displacement Measure of Voter Power
Exhibit 2.15: Potential Displacement Via Single Voter
Exhibit 2.16: Electoral College Power Under Alternative Theories
a.

4.

EFFICIENCY ASPECTS OF FAIRNESS
STATE OF IOWA v. HENRY PARRISH

5.

“PATERNALISM” IN THE LAW

92
92
94
94
95
96
96
96
100

CH. 3: INTERTEMPORAL COSTS AND BENEFITS

103

A.

INTEREST RATES AND “PRESENT VALUES”

103

Exhibit 3.1: (1+r)n Compound Interest Growth Factors

105

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Goetz, Law and Economics

Exhibit 3.2: 1/(1+r)n Discount Factors

B.

VALUING THE BENEFITS OF INTERESTS IN LAND

106

108

1.

DETERMINING THE VALUE OF A LEASEHOLD

108

2.

VALUING A PROPERTY ENCUMBERED BY A LEASE

108

C.

INTEREST ON DAMAGES AND PENALTIES

109

1.

PREJUDGMENT INTEREST ON DAMAGES
BUSIK v. LEVINE

109
109

2.

“BACK DOOR” PREJUDGMENT INTEREST?
UNITED TELECOMMUNICATIONS, INC. v. AMERICAN
TELEVISION AND COMMUNICATIONS CORP.

113
113
113

3.

PREJUDGMENT INTEREST ON PENALTIES

115

D.

E.
1.

EVALUATING LOST FUTURE INCOME AS DAMAGES

116

Exhibit 3.3: Lost Income Damages, Assumption Set #1
Exhibit 3.4: Lost Income Damages, Assumption Set #2
BEAULIEU v. ELLIOTT
DOCA v. MARINA MERCANTE NICARAGUENSE, S.A.

117
118
119
123

COMBINED UNCERTAINTY AND DISCOUNTING

129

Introductory Considerations
Tintd Hypothetical
Exhibit 3.5: Tintds’ Probability of Survival to Various Birthdays
b. Annuity Hypothetical
c.
Life Tenancy and Remainder Rights
a.

129

130
130
130
131

2.

AVERAGE vs. actuarily expected LIFE earnings
Exhibit 3.6: Average Lifespan vs. Actuarial Calculations

132
133

3.

RISK SELECTION AND RISK COMPENSATION
Exhibit 3.7: Analysis of Rentals

134
135

4.

DEFAULT COST UNDER “BACKDOOR” INTEREST SCHEMES
Exhibit 3.8: The “Time Price” Interest Subterfuge

136
136

F.

G.

TAX TREATMENT OF TORT DAMAGES

139

DeLUCCA v. UNITED STATES

139

FAIRNESS IN EMPLOYEE BENEFITS

142


Table of Contents

v

1.

Contributions to Pension Plans
LOS ANGELES DEPT. OF WATER AND POWER v. MANHART

142
142

2.

CONSTRUING THE AGE DISCRIMINATION IN EMPLOYMENT ACT

145

CH. 4: MAPPINGS AND “DEMAND” DECISIONS

147

A.

147

TOPOGRAPHICAL MAP READING

1.

Decisions Based on Spatial Locations
Exhibit 4.1 – Topographic Map Showing Relevant Features

147
148

2.

INDIFFERENCE CURVE MODELS AND MARKET DECISIONS
Exhibit 4.2: Economic Topography and Constraints

149
149

B.

GROUP DECISIONS UNDER MAJORITY RULE

151

1.
2.

“Rational” Group Preferences
MODELING OF VOTING DECISIONS
Topographic Model of 3-Person Majority Rule Decisions
Exhibit 4.3 – Topographic Map of Budgetary Decisionmaking
b. A MATRIX MODEL OF VOTE TRADING
Exhibit 4.4 – Voters’ Benefit Changes For Measures A & B
a.

C.

D.

E.

F.

G.

151
152
152

152
153
154

DECISIONMAKING IN THE COURTS

155

STATE OF MISSOURI v. BARTON
HARRIS v. RIVERA

155
156

EDGEWORTH BOX ANALYSIS OF CONTRACTS

158

CONTRACTUAL REALLOCATION THROUGH “EFFICIENT BREACH”
Exhibit 4.5 – Indifference Curve Model of Efficient Breach

158
159

CONSUMER CHOICE: MODELING PROMISSORY RELIANCE

161

Exhibit 4.6 – Intertemporal Model of Promissory Reliance

162

PERMISSIBLE AND IMPERMISSIBLE EFFECTS OF GOVERNMENT GRANTS
164
MATHEWS et al. v. MASSELL
TILTON v. RICHARDSON
Hypothetical: Christian Friars Wine Sales to Military

164
167
172

BRIBES VERSUS THREATS

172

UNITED STATES v. BUTLER
STEWARD MACHINE CO. v. DAVIS
CARROTS vs. STICKS

173
176
177


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Goetz, Law and Economics

H.

3.

MEASURING RESPONSIVENESS: ELASTICITIES

179

HARRIS v. McRAE
UNITED STATES v. E. I. DU PONT DE NEMOURS & CO.

181
182

LEGAL APPLICATIONS FROM DEMAND THEORY

184

CH. 5: CHANNELING BEHAVIOR VIA LEGAL INCENTIVES

187

A.

187

TORT LIABILITY MODELS

1.

THE LEARNED HAND RULE: A MARGINAL COST-BENEFIT FORMULATION

Exhibit 5.1 – Marginal Cost and Marginal Benefit of Precautions

187
188

2.

THE HYPOTHETICAL MODEL UNDERLYING THE DIAGRAMS
Exhibit 5.2: Effect of Recognizing Only 75% of Actual Harm

189
190

ERRORS IN THE APPLICATION OF TORT LAW
Incorrect Assessment Of Damages

190
190

Mistakes In Applying The Liability Standard
Exhibit 5.3: Probability of Jury Requiring Care Level
Exhibit 5.4: Behavior Effects of Errors Regarding Care Standard

191
192
194

3.
a.
4.

B.

MULTI-PARTY HARM PRODUCTION FUNCTIONS

195

1.

Precautions That Minimize Net Social Cost of Accidents
Exhibit 5.5 – Multiparty Social Cost Function #1

195
196

2.

Comparative Negligence
Exhibit 5.6 – Multiparty Social Cost Function #2
BENTZLER v. BRAUN
VICTOR SCHWARTZ, COMPARATIVE NEGLIGENCE, p. 297
STATE v. KAATZ

197
198
200
200
201

C.

THE “LEVEL” OR QUANTITATIVE PROBLEM

202

GREENLAWN NEIGHBORHOOD ASSOCIATION v. FIRST
GUARANTY BANK

204
204

TAKING COST-MINIMIZATION SERIOUSLY(?)

205

The Case Of Innocente v. Vinho
Drunks Won’t Let The Preacher Alone

205
206

PROMISE-BREAKING ANALYZED AS A TORT

206

D.

E.
1.

Economically Optimal Damages For Broken Promises

206

2.

Sec. 90, Restatement Of Contracts

211


Table of Contents
CENCO, INC. v. SEIDMAN & SEIDMAN
HYPOTHETICAL: PERILS OF A TAXJACQUES
PERFORMANCE DEFINITION AND RELATIONAL CONTRACTING
Exhibit 5.7
Exhibit 5.8
BEST EFFORTS PROVISIONS
Exhibit 5.9
HYPOTHETICAL: INTERWOOD v. FORREST LUMBER
BLOOR v. FALSTAFF BREWING CO.

vii
212
215
216
219
221
224
225

228
229

CH. 6: SUPPLY AND SYSTEMIC INTERACTIONS

236

A.

236

PRODUCTION COSTS AND CONTRACT BREACH

1.

Cost Conditions For A Firm Producing Standprods
Exhibit 6.1: Costs at Alternative Outputs

236
237

2.

Cases About Damages for Breaches of Duty
JERICHO SASH AND DOOR CO. v. BUILDING ERECTORS, INC.
NOBS CHEMICAL, U.S.A., INC. v. KOPPERS CO., INC.
CURT’S TRUCKING CO. v. CITY OF ANCHORAGE
LUND v. COMMONWEALTH

238

238
238
240
243

B.

ADJUSTMENT OF A COMPETITIVE INDUSTRY

246

1.
a.

b.
c.
d.
e.

2.

C.

D.

A Simons Model of Competitive Equilibrium
Part I. Initial Equilibrium State
Exhibit 6.2: Graph of Firm’s Cost Curves
Exhibit 6.3: Short-run Equilibrium of Supply and Demand
Partial Displacement And Short-Run Equilibrium Adjustment

Exhibit 6.4: Costs to Firm Paying ASD Royalty
Progress Toward New Equilibrium
Additional Implications
A Simple Mathematical Model [Optional]
Exhibit 6.4b: Solutions of Market Model

246
246
247
248
248
249
249
249
250
252

Bankruptcy Laws And Fixed Costs

252

INCIDENCE ANALYSIS: SHIFTING AND PASSING ON

253

HANOVER SHOE, INC. v. UNITED SHOE MACHINERY CORP.
ILLINOIS BRICK CO. v. ILLINOIS

254
255

ANTICOMPETITIVE SUPPLY RESTRICTION

258

Exhibit 6.5: Expansion versus Market Spoilage
CLARK v. UNIVERSAL BUILDERS, INC.
STATEMENT OF U.S. DEPT. OF TRANSPORTATION BEFORE THE INTERSTATE COMMERCE
COMMISSION, WESTERN COAL INVESTIGATION-GUIDELINES FOR RAILROAD RATE
STRUCTURE
GHEN v. RICH
CONSTRUCTION INDUSTRY ASSOCIATION OF SONOMA COUNTY v. CITY OF PETALUMA

259
269

278
280
283


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Goetz, Law and Economics

Exhibit 6.2a: Correctly Graphed Cost Curves
Exhibit 6.3a: Completed Graph of Demand and Shifting Supply Curves

289
289

CH. 1: ANALYZING CHOICE UNDER ALTERNATIVE RULES
A. INTRODUCTORY CONSIDERATIONS
There can be little doubt that one primary purpose of legal systems is to modify human behavior, to
induce at least some people to act in ways that they would not choose but for the pressure of legal incentives or disincentives. If this behavior-modification or “channeling” function of law is truly important,
then it also becomes imperative to understand the predictable behavioral implications of alternative legal
doctrines and policies. When a particular rule change is enacted, exactly what will happen? Or, if we
cannot predict “exactly” what will happen, can we make any useful generalizations at all about the results
of a proposed modification in law? And if it is indeed impossible to make useful predictions about consequences, then on what grounds are institutional changes to be advocated?
These observations suggest that the study of Law can be thought of as having a close affinity to the
social sciences. Jurisprudence is, after all, inevitably concerned with predicting and describing the behavior of human beings under alternative institutional arrangements. Increased awareness of this is precisely why the nexus between Law and traditional social sciences, especially Economics, has become the
focus of intensified interest in recent years. Methodological tools and concepts of the social sciences are
increasingly applied in legal scholarship because they provide insights about the interaction of human
beings judges, parties litigant, potential tortfeasors, etc.-as they confront alternative legal rules.
The use of economics in legal analysis is sometimes viewed with alarm and alleged to be infected with
ideological connotations. Of course, any “approach” to legal analysis can be, and frequently is, bent to
serve ideological purposes. Just bear in mind that economic analysis is no more and no less subject to this
danger than many another tool of intellectual inquiry. Whatever the goals of its users, the power of economic analysis to predict and describe many facets of human behavior has no necessary link with value
judgments about what conduct or institutions should be classified as good, bad, or indifferent. One can,
after all, describe in essentially neutral fashion the objective implications of alternative rule systems
without sitting in judgment on the results themselves. Occasionally, the mere laying bare of policy implications seems to lead rather directly to value judgments, but this is not an inherent characteristic of the
analysis itself; rather, it reflects what is frequently the natural reaction of an observer to any revelatory
process.
Economists use special terms of art to distinguish descriptive-predictive analysis from prescriptivejudgmental statements, labeling the two analytical modes as “positive economics” and “normative economics,” respectively. Inevitably, objective economic analysis and subjective opinion tend to become
intertangled in the hands of many practitioners. Nevertheless, an expert in positive social science analysis
does not, merely by virtue of his technical expertise, warrant having any greater-than-ordinary deference
paid to whatever purely normative opinions he may from time to time intermingle with his analysis.
On the other hand, a reasonable ability to describe the implications of alternatives does seem to be a
necessary precondition for competent formation of value ;judgments, if forming value judgments is what

one ultimately is interested in doing. After all, unless the objective consequences of alternatives are first
correctly understood, how can subjective value weightings be rationally and intelligently attached? One
useful result of analysis therefore is to expose counterintuitive effects or ill-considered indirect consequences of a policy. Indeed, it is not uncommon to hear economic reasoning used to suggest that a legal
policy adopted in pursuit of some goal is unintentionally counterproductive. Hence, although prediction is
not itself an inherently normative act, it serves as an essential input into the process wherein people ultimately arrive at reasoned value judgments about law-or any other public policies, for that matter. From
this point of view, predictions about the economic consequences of legal decisions are a valid and useful
part of the “means to ends” debate in a legislative or judicial proceeding. Of course, in an adversary proc-


2

ANALYZING CHOICE UNDER ALTERNATIVE RULES

Chapter 1

ess, it is perhaps unsurprising that the predictive inputs are frequently selective and self-serving. Still,
such inputs are no more and no less than specialized and occasionally quite persuasive formal tools of
legal argumentation. Potentially powerful tools of legal argumentation can be ignored only at one’s peril.
In fact, the probability of having to deal with economic reasoning in law seems to be growing, whether in
the form of affirmative arguments to be advanced and supported or as allegations that someone else raises
and which, therefore, must be probed, criticized, and rebutted.
Advocacy is not the only use of economic-type behavioral analysis, however. Sometimes the application is quite simply educative and explanatory, an attempt to understand something or reconcile it with
apparently conflicting information. For instance, a pervasive concern in legal studies is the role of coercion. Behavioral strictures rise above the status of mere exhortations and become “laws” precisely
because they are backed by a sanction or coercive force. Yet, in a democratic society, laws supposedly
arise out of the consent of the governed. To many, this smacks of mystery, or at least paradox. Why
would people consent to-and, presumably, benefit from-a system of coercion? Some of the early analysis
in this chapter is directed precisely at the question of why self-imposed coercion is a plausible and
voluntarily chosen response to a wide class of societal problems.
Behavioral analysis frequently reveals that results which appear to have been chosen freely and
voluntarily are, on closer inspection, not so greatly desired as they superficially seem. This is a very important realization because the fact that a decisionmaker freely chooses an option is often offered as an

allegedly persuasive empirical proof that the chosen option must be “better” than the other available
choices. Otherwise, why did the person choose what he did rather than something else? In fact, whereas
there is indeed a kernel of truth in that somewhat Panglossian argument, it is at best a prima facie argument or presumption, subject to qualifications that are of great relevance in precisely the factual circumstances that typify many legal applications. Even in this initial chapter, we shall see that circumstances
frequently induce people to choose results that they would certainly regard as “inferior” to other available
results.
Another recognizable objective of economic analysis in Law is that of mere explanation. Under this
rubric, one may hypothesize about why people did historically make a particular policy choice without
also necessarily endorsing the values of the original decisionmakers. This involves a process of working
backwards, of discovering a plausible rationale for observed behavior, of ferreting out what may have
been the motivation for a law. One is then free to take the additional step of approving or disapproving
what are perceived as the underlying objectives of those who actually made the choices. Becoming aware
of an underlying systematic basis for some class of phenomena can powerfully assist one in learning a
body of doctrine, manipulating it, appreciating its nuances, and even predicting its evolution in response
to changing conditions.
This chapter introduces some elementary concepts that will be useful in reasoning about legal phenomena in terms of behavioral science concepts. Initially, the behavioral science concepts employed are not
notably “economic” in character. Although the vocabulary of the economist’s conceptual bag of tools has
become increasingly important in legal applications, the application of economic terminology should not
imply any claim that the phenomena being analyzed are necessarily economic in the narrow sense of the
term. In fact, it just happens that certain conceptual tools created by economists for the analysis of explicitly economic transactions can usefully be adapted to the legal environment. Legal issues frequently do
have an explicitly economic component, of course. Nonetheless, if the methodology presented below is
properly understood, it can legitimately be applied in many areas where mere economic motivation would
be a gross oversimplification. In many cases, the language of economics represents merely the application
of a specialized tool of formal logic, a deducing of conclusions from premises in a way somewhat akin to
the still more abstract methods of symbolic logic and mathematics upon which, in turn, economic theory
itself draws. It is perhaps true that the more formal and elegant a mode of analysis, the more an unwary
person runs the risk of being overly dazzled. On the other hand, formal reasoning is valuable precisely


Chapter 1

ANALYZING CHOICE UNDER ALTERNATIVE RULES

3

because it permits a careful observer to scrutinize critically both the premises and the logical links that are
alleged to justify certain conclusions.
Finally, one should be sensitive to the limits of economic argumentation in legal contexts, even when
“economic” is construed in its most expansive and generous sense. In some circumstances, arguments
based on economic reasoning will have undeniable relevance and potent persuasive force. In other situations, economic factors may be of relatively trivial weight as compared to amorphous-yet perfectly validethical, moral or even viscerally instinctive notions of what is right and just. As with any other source of
legal arguments, economic factors must ultimately be evaluated through each individual’s own views of
their relevance and weight. Economic analysis is not a single great searchlight that will penetrate and
illuminate every nook and cranny of the law, but neither is any other “approach,” whether it be rooted in
ethics, sociology, legal history, or some other discipline that can be brought to bear on legal problems.
Since this is a book about economic reasoning in law, practical constraints will impose what may occasionally resemble methodological tunnel vision. With only that caveat, the reader is credited with the
good sense to integrate, where necessary, the narrowly focused materials that follow into a more fully
articulated intellectual framework.
The material in this book is not intended to be elegant or highly technical economics. An attempt is
made to develop and apply only that limited set of economic-type constructs that is most useful in legal
reasoning. Even so, there is relatively short shrift given to many traditional economic topics that are
adequately treated elsewhere, in standard economic textbooks at an elementary or intermediate level. The
analytic concepts are introduced here in a carefully phased process wherein the applications grow progressively more sophisticated. Considerable cohesiveness and intrinsic interest has been designed into
these legal applications, since the intent is for this to be genuinely a law book rather than intermediate
economic theory thinly cloaked with market-linked legal issues. But the reader should be warned that
communication of an underlying set of analytic principles is the real goal and the organizing principle of
these pages is the economics, not the law. Accordingly, communication of economic content is frequently
pursued in ways detrimental to a potentially more informative treatment of the substantive law involved.
Several of the first few concepts introduced below are originally drawn from game theory. Why give
such a primacy of place to game theory? A standard dictionary definition of a game is: “a contest, physical or mental, according to set rules, undertaken for amusement or for a stake.” Two elements of that
definition should be especially noted. One is that games are explicitly defined as behavioral situations
governed by rules. The second is that game theory deals neither exclusively nor even primarily with contests undertaken for amusement; rather, it analyzes the behavior of “players” in serious conflict situations,

frequently for heavy stakes. Conflict within a set of rules is what a great deal of the law is really about.
Some of the “games” affected are played out in a marketplace where buyers and sellers compete for
resources subject to a set of property and trading rules. This is the traditional domain of economic analysis. Legal proceedings can themselves be conceptualized as games, governed by their own peculiar system of rules, entitlements, costs, etc. Many of the underlying conflict situations giving rise to legal proceedings can also be understood as games. In any case, students of the Law ought to be fundamentally
interested in how the strategies of players change and how the predicted outcomes vary as the applicable
rules of various law-related “games” are modified.
QUESTIONS
1. There are many situations in which some agenda of societal goals and the trade-offs between them
has already been fully articulated and predetermined. A legal analyst’s role, therefore, is merely to
offer counsel to decisionmakers regarding the advisability of alternative laws as means to these ends.
a. What real-world jobs for a lawyer fit the above scenario? In what respects is predictive competence
necessary?


4

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Chapter 1

b. Drug addicts are responsible for a large amount of crime. This crime is thought to be motivated by
the addicts’ eagerness to “earn” the income necessary to support an expensive drug habit. In 1973,
the State of New York passed tough new mandatory sentencing provisions which increased the
penalties for drug distribution. It is plausible to assume that the legislators were attempting to
reduce the availability of drugs and the attendant crime problem. Are tougher drug laws an effective means to that end? Does your answer depend on empirical data?
c. Supply some specific examples wherein it can persuasively be argued that a statute or common law
rule adopted as a means to an identifiable end is actually detrimental to that end. Can you supply
another example of a law that has unintended “byproduct” consequences that substantially vitiate
the benefits of what was originally viewed as its direct or primary objective?
2. You are a basketball fan. A proposal is made to penalize a team two points per inch or fraction
thereof for the number of inches by which the average height of its players used in a game exceeds

76.
a. Could a basketball coach help you in describing what effect this rule change would have on how the
game is played? What kinds of things would the “expert” be able to tell you that you couldn’t figure out for yourself? Would you expect any surprises? (E.g., can you advance any argument that
suggests that having one or more real giants on a team would become more important than ever
before?)
b. Once he had expounded on the consequences to the game, to what extent would you be willing further to defer to the expert’s opinion as to whether the resultant changes would make the game better or worse? If possible, provide an example of a sports rule wherein you suspect that the preferences of coaches and fans are antagonistic.
c. Are the “experts” always right in predicting consequences? NCAA rules allowed conferences to use
several kinds of “experimental” basketball rules-such as the three-point shot and the time clock-for
the first time during the 1982-83 college season. If you do not remember yourself, ask a friend
who is a real fan. When are experts most likely to be right or to be wrong?
3. Richard Posner and others have argued that common law legal rules implement goals of “economic
efficiency.”
The rules assigning property rights and determining liability, the procedures for resolving legal
disputes, the constraints on law enforcers, methods of computing damages and determining the
availability of injunctive relief-these and other important elements of the legal system can best be
understood as attempts, though rarely acknowledged as such, to promote an efficient allocation
of resources.1
This position is, as might be imagined, a controversial one. In fact, the very sense in which the term economic efficiency should be understood is itself subject to some debate.
a. Suppose that economic efficiency were defined as a situation in which potential economic gains
were fully exploited or, what is pretty much the same thing, “wasteful” conduct were discouraged
1

Posner, "The Economic Approach to Law," 53 Texas L.Rev. 757, 764 (1975). See also, Posner, "Some Uses and
Abuses of Economics in Law, 46 U.Chi.L.Rev. 281, 288-89 (1979). Other scholars have advanced similar theories
although they differ, and to some extent disagree, among themselves with respect to methodology and details of the
theory. These include: Rubin, "Why is the Common Law Efficient?," 6 J.Legal Stud. 51 (1977); Priest, "The
Common Law Process and the Selection of Efficient Rules," 6 J.Legal Stud. 65 (1977); Goodman, "An Economic
Theory of Evaluation of the Common Law," 7 J.Legal Stud. 393 (1978); and Priest, "Selective Characteristics of
Litigation," 9 J.Legal Stud. 399 (1980). A discussion of the difficulty of proving the efficiency hypothesis may be
found in Kornhauser, "A Guide to the Perplexed Claims of Efficiency in the Law," 8 Hofstra L.Rev. 591, 610-21

(1980).


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and avoided. How plausible does it seem to you that a large part of common law doctrines might
be explicable in terms of economic efficiency goals?
b. One seldom finds explicit use of economic analysis in judicial decisions, a fact which does not
seem to support the assertion that economic considerations are determinants of judicial policy. The
following remark by Prof. Neil Komesar may be interpreted as casting some doubt on the strength
of that evidence:
Traditional legal analysis teaches that the reasons articulated by the decisionmaker are seldom sufficient-and are sometimes irrelevant-as indicators of the actual determinants of decisions. Judicial opinions are more often observations to be explained than sources of explanation. They yield insights only to one who can approach them systematically.2
What do you think? To what extent are written opinions themselves probative as to the underlying
motivation of judicial decisions?
c. One objection to the efficiency hypothesis about common law formation is that many jurists never
have and never will know very much about economics. To what extent would a Darwinian-type
“survival of the fittest” explanation meet that objection?3
d. Assume that the common law efficiency hypothesis were persuasively established as a more or less
accurate reflection of historical fact, but you are a Marxist and regard the pursuit of economic efficiency as a vicious capitalistic excuse for grinding the faces of the poor. Would knowing the economic efficiency implications of various legal rules have any value to you as a lawyer?
4. The following rule is proposed: when property subject to a security interest is claimed by a creditor
and sold, the debtor must be credited with the actual proceeds of the resale or the fair retail value,
whichever is higher.
a. What are the implications of such a rule if adopted? Are such implications likely to be important in
determining the decision? If your answer would be different depending on the forum (court, legislature, regulatory commission, etc.), indicate why.
b. Would you know how to cross-examine an economist testifying as to these implications? If the
forum were a court, would expert testimony of that type be allowed?

B. ELEMENTARY GAME THEORY
1. THE PRISONER’S DILEMMA
The following scenario illustrates a famous game-theoretic model that is attributed to the mathematician A. W. Tucker. Widely known as the “Prisoner’s Dilemma,” this situation, together with several
closely related fact patterns, provides powerful insights into behavioral problems that have importance in
the law.4 The scenario presented here is embellished slightly for pedagogical purposes but, as the title
suggests, closely follows Tucker’s original anecdote.

2

Komesar, In Search of a General Approach to Legal Analysis: A Comparative Institutional Approach," 79 Mich.L.
Rev. 1350, 1354-55 (1981).
3
For instance, Rubin, supra, posits an evolutionary mechanism guided by the decisions of the litigants rather than
the judges. The evolutionary approach is criticized in Cooter and Kornhauser, "Can Litigation Improve the Law
Without the Help of Judges," 9 J.Legal Stud. 235 (1980).
4
There is an extensive literature dealing with this famous game-theoretic concept. For general discussions at a
reasonably accessible level, see R. Luce and H. Raiffa, Games and Decisions, 94-102 (1967); A Rapoport and A.
Chamah, Prisoner's Dilemma (1965); A. Rapoport, N-Person Game Theory (1970).


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Imagine that you are an urban clerical worker who stops off in a downtown bar after working late one
night. You encounter a kindred soul, hitherto a perfect stranger. In the course of having several drinks, the
two of you commiserate over your mutual senses of extreme financial deprivation. One thing leads to

another and, after suitably cautious circumlocutions, this new friend finally suggests that there might be a
very nice gain indeed from knocking over a certain downtown jewelry store. In true Hollywood fashion,
the fadeout of one scene depicts the larcenous proposal. Then, cut to the next scene wherein the two of
you are braced against a building wall being frisked during an arrest by the Metropolitan Police. The jewelry store alarm bell is ringing and a few nice rope-of-gold necklaces are drooping accusingly out of your
pocket.
QUESTIONS
1. First a predictive question. If it were necessary to complete the “script” of the above scenario, what is
a plausible ending to the story? How sure are you?
c. First, assume that an agreement between the two prisoners not to testify is unenforceable by any
sanction, whether legal or retributive. Would both prisoners testify? Neither one? How would they
behave and why? How would you behave under similar circumstances? Does it matter whether or
not the prisoners are allowed ample opportunity to communicate with each other?
d. If an agreement not to talk is unenforceable legally, one or both parties may nonetheless attempt to
convince the other that an agreement not to testify will be enforced by subsequent retribution
against the party who “squeals.” Assess the credibility of this threat. Would the prisoners be better
off if they both belonged to the Mafia?
e. Suppose that a court of law would provide traditional damage remedies for any agreement between
the prisoners. Specifically, the prisoners could make a legally binding contract and the party who
breached the contract would be held liable for damages suffered by the breachee. This possibility
suggests another predictive question: Exactly what contract would you expect them to make?
f. How can the prisoner’s dilemma concept be applied more generally to the whole field of executory
contracts? What relationship is there to the traditional legal concept of “reliance”?5
2. Now some “normative” considerations.
a. “Should” such a contract between prisoners be enforceable? Why?
b. A corollary question. Is it appropriate that prosecutors be permitted to place prisoners in conditions
that produce a Prisoner’s Dilemma?
3. Now a conceptualization. Assume that you are not able to use the above scenario as an illustration.
How would you explain or define a Prisoner’s Dilemma to someone else?
4. A policy application. It has sometimes been suggested that the same attorney should not be permitted
to represent two co-defendants being tried in connection with the same criminal incident.6 The thesis

is that conflicts of interest inevitably arise between two defendants such that no common position
can fairly represent the interests of both clients.
a. What relevance does the Prisoner’s Dilemma have to this proposed ban against joint representation?
In the text above, a “dilemma” was created by the prosecutor’s structuring of a possible deal. Does
joint representation address difficulties that may arise merely out of the facts of the case and the
applicable law?
5

See the application to the law of contract in Birmingham, “Legal and Moral Duty in Game Theory: Common Law
Contract and Chinese Analogies,” 18 Buffalo L.Rev. 99, 105-10 (1968-69).
6
See, for example, Geer, “Representation of Multiple Criminal Defendants: Conflicts of Interest and the
Professional Responsibilities of the Defense Attorney,” 62 Minn.L.Rev. 119 (1978); Gary T. Lowenthal, "Joint
Representation in Criminal Cases: A Critical Appraisal," 64 Va.L.Rev. 939 (1978).


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b. Prof. Gary Lowenthal observes the following:
To the extent that counsel do not cooperate with each other, it reasonably can be inferred
that the interests of the clients conflict. When clients have conflicting interests, one attorney representing all of the defendants can present a unified strategy only at the expense of
prejudicing one or more of the clients.
Lowenthal, supra, at 986. Do you agree?
5. Finally, an attempt to generalize or analogize: describe some other fact situation wherein the participants seem to be confronted with a behavioral problem similar to the Prisoner’s Dilemma.
a. THE STUDENT’S DILEMMA: UNIVERSITY v. EAGER
The following facts describe a situation that arose in a science course at a large state university:

The University has a rule that penalizes cheating by dismissal and the notation “Dismissed for Cheating”
on the offender’s transcript.
The mechanics of the examination process are such that it is very easy to cheat. There is a negligible risk
of any penalty; the probability of being caught is very close to zero, but not zero.
Grades are distributed strictly on a required curve: A to the highest 10%, B+ to the next 20%, etc.
The course is a key subject required for pre-med students and is known to be an important consideration
in the process of medical school admissions reviews. Hence, the benefits from high grades and the
penalties for low ones are exceptionally great.
Lightning strikes! While the class is taking the final examination, the proctoring system manifests one
of its rare, seemingly spasmodic surges into action. Fourth-year student Edward L. Eager is caught in flagrante delicto. The evidence that he did in fact cheat is absolutely conclusive; consequently, Ed faces
dismissal.
Chris Pensive, another student in the class, is troubled by Ed’s predicament and was overheard to make
the following comment.
“Something is wrong, all out of proportion, with the way Ed is being treated. Maybe what he did
wasn’t right, but he’s being punished almost as if he were a criminal. Under the circumstances, his
behavior just doesn’t seem that bad to me. Ed was almost under duress, almost compelled to do what
he did. I don’t blame him. I blame the school for holding exams like that.”
Ed now faces an administrative hearing prior to the imposition of the penalty pursuant to University
rules.
QUESTIONS
1. Is a Prisoner’s Dilemma among the students involved here? Or is the situation “something like” a
PD?
2. How would you defend Ed if assigned as his counsel at the hearing? Is the University arguably at
fault? Is Ed subjected to an irresistible temptation? Is this a case of “self defense”?
3. Chris apparently finds the penalty disproportionate. How should an appropriate penalty ideally be
determined?
4. Bribery of foreign officials by the agents of U. S. corporations operating abroad is subject to sanction
under U. S. law. Does this bear any similarity to the Ed Eager scenario?
5. What are some real-world analogues of University v. Eager? What legal or policy issues are suggested?

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b. THE PRISONER’S DILEMMA AS A MATRIX MODEL
The use of models is almost ubiquitous in social science. In one sense, the term “model” has almost its
vernacular meaning of a representation. When used in a theoretical context, however, a model transcends
mere representation; indeed, it may to some extent deliberately sacrifice accuracy of representation for a
more abstract and general description that highlights the most important elements in the phenomenon
being “modeled.” Models may even be caricatures, having the same goal as a deft cartoonist who, with a
few expertly chosen but highly oversimplified lines, seeks to convey a meaning more clearly than through
a photographic likeness. It must already be apparent that the Prisoner’s Dilemma is a conceptual model, a
paradigm or pattern with potentially wide application. In short, the insights of the PD can be analogized to
many other interesting situations, as the Ed Eager scenario in the last section exemplifies. It is interesting
to see, however, that the paradigm of the Prisoner’s Dilemma can itself be modeled in several different
ways, varying greatly in their degree of formality. One approach is the one just used: simply to tell the
story, employing only ordinary English words similar to those used in the text above. Alternative descriptions, or models, of the same situation may convey additional insights, or at least conceptualize the situation with greater clarity. This possibility will probably be apparent as we now-construct a more formal
and compact rendition of the same Prisoner’s Dilemma conflict.
The Prisoner’s Dilemma is frequently presented in the form of a matrix model of the type shown in
Exhibit 1.1. In this simple form of model, the rows of the matrix represent the possible choices open to a
particular prisoner: either Testify or Silence. The columns represent the exogenously controlled circumstances. Hence, the “other” prisoner will either have chosen Testify or Silence. In creating these matrix
models, the same general convention is usually followed: choices or “strategies” under the decisionmaker’s own control appear on the rows while the externally-controlled “state of nature” is represented by
the columns. Each “cell” formed by the intersections of the rows and columns therefore corresponds to a
unique combination of the individual’s own decision and the external conditions imposed on him exogenously, in this case by the other person’s choice.

Exhibit 1.1: PD Matrix Model
Your Own Behavior

SILENCE
TESTIFY

Behavior by the Other Prisoner
SILENCE
TESTIFY
-0.75
-5.0
0.0
-3.0

Do the row and column labels in Exhibit 1.1 encompass all of the relevant possibilities both for the
choosing individual’s own choice and the other individual’s choice? If so, then the resulting four cells
properly represent the four possible outcomes of the Prisoner’s Dilemma. Such a representation of the
possible choices and outcomes is an important first step in modeling. In more formal language, this process is frequently called identification of the “choice space” or “opportunity set.”
Once the possible outcomes are thus identified, the implications of each outcome can also be indicated.
In Exhibit 1.1, this is accomplished by placing a number in each cell to tell the outcome or “payoff” in
terms of years spent in jail. Other kinds of numbers might be more appropriate for certain purposes. (Can
you think of any drawbacks of using years as opposed to something else?)
In any event, the resulting matrix model does give a concise kind of “Picture” of the situation faced by
any decisionmaker. It is now easy to see that the Testify strategy has what game theorists call the quality
of “dominance”: no matter which column is assumed, the Testify strategy row always results in the best
payoff, i.e., the lowest jail sentence. [Place a circle around the lowest jail sentence in each column of
Exhibit 1.1.] In other words, dominance exists when, no matter what the external situation is (as represented by the columns), the “best” strategy for the decisionmaker is always the same row. This presence


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of dominance is why we might reasonably predict that a prisoner who understands the situation will
choose to Testify.
But the other prisoner faces the same kind of matrix-a condition known as “symmetry” of the payoff
matrix for the two individuals and hence can also be predicted to Testify. That enables us to advance a
step further and hazard a prediction about the particular outcome of the game that we are most likely to
see: because Testify is a dominant strategy for both players, the expected “solution” of the game will be
the lower right-hand cell. This, of course, is precisely what the Prosecutor’s office hopes for and is the
reason why it has structured the “rules” of the game the way they are. A classical Prisoner’s Dilemma,
then, falls into the wider category of games with a predictable outcome or “solution.” In economic
models, such a solution will be called an “equilibrium” outcome.
Not all models have determinate solutions or equilibrium outcomes. [The “Chicken” game described
later in this chapter will be one that does not.] Even when there does exist what seems to be a determinate
theoretical solution, one should be wary of the fact that models are almost always abstractions and simplifications of reality. Still, within appropriate limits, models are powerful analytic tools because they help
clarify what forces are at work and how these forces interact. Hence, it is properly cautious to think of
models as formalized descriptions of “what tends to emerge” under specified behavioral conditions and
factual assumptions.
As we have already seen, models may also be articulated in mere vernacular speech rather than through
formal constructions. Lawyers, after all, traditionally pride themselves on their ability to distinguish,
deduce, and generally massage and manipulate the English language during any process of legal analysis.
One thesis of these pages, however, is that there is frequently some advantage in going through a more
formal modeling process, of “writing down” the behavioral conditions in slightly more technical fashion.
For instance, do you find that Exhibit 1.1 conveys the essence of the Prisoner’s Dilemma game more
clearly than mere words? Most, though not all, people feel that it does. The construction just used, the
matrix model, is a relatively simple one. As subsequent situations are analyzed, the modeling will require
many additional building-blocks of a conceptual type. These building-block concepts are labels and
analytical devices that provide tools of thought in much the same way that having more brushes and
colors enables an artist to paint better pictures. Equally important, many of the concepts are concise and
convenient means of communicating about complex situations with others who “speak the language,” just

as terms such as negligence, consideration, and reliance are key concepts that facilitate communication
among students of the law. That is why it is important to have the patience to learn a certain amount of
behavioral science jargon and terminology.
At the same time, a caveat should be issued as we undertake to add to the arsenal of technical terms and
concepts: beware of using technical jargon in an inappropriate forum. Economic jargon is frequently not
only incommunicative but, worse yet, runs the risk of arousing negative reactions from those—including
senior partners and powerful judges—who have not themselves assimilated the language. After working
out the implications of a situation in more rigorous terms, therefore, the legal practitioner is often confronted by the necessity to translate arguments and conclusions into more traditional legal terms.
Although the translation process may require care and sensitivity, what truly makes sense in one language
ought to be susceptible to communication in another form, even if less elegantly. In sum, rigorous terms
of art may be ideal in working out one’s own personal analysis, but ultimately the language of argument
and persuasion must be carefully adapted to its audience.
c. THE “PRISONER’S DILEMMA” DEFINED
Labeling various behavioral conflicts with names such as Prisoner’s Dilemma is merely a technique of
classifying situations in a way that may lead to generalizable insights; one should not take the strict
requirements of the classic “models” or paradigms too seriously. Nevertheless, a significant advantage of


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formalizing definitions is that distinctions between otherwise similar situations become apparent. Note
that, although we have used the concept and discussed it at some length, a Prisoner’s Dilemma has not yet
been formally defined. Although you may think that you more or less know what one is, could you really
distinguish a classic PD-type situation from just a garden-variety “tough spot”? A rigorous formal definition should clarify just what are the important elements of the phenomenon being discussed. Once these
elements of the definition are isolated, one can more easily recognize relevant distinctions among closely
related phenomena. Looking ahead, a formal definition will suggest why it is worth distinguishing

Prisoner’s Dilemma from one of its close lineal descendants in the game theory family, the game of
Chicken.
In order to construct an appropriate definition, the structure of the Prisoner’s Dilemma game will once
more be presented in its now-familiar matrix form. In Exhibit 1.2, the standard conventions are used
whereby the rows designate the strategies, the things the player does control, while the columns reflect the
“states of nature” that are externally controlled. “Cooperate” is the strategy that involves cooperation
among the people in the Dilemma and “Defect” is any departure from this mutually beneficial behavior.
By substituting abstract symbols for the numbers in the cells, however, a great deal of additional
generality can be derived from the model. Hence, the algebraic symbols a, b, c, and d are now used to
represent the payoffs associated with each box or “cell” of the matrix. Note that these symbols may still
signify years in jail, as postulated in the original scenario. They are also consistent, however, with payoffs
denominated in other kinds of units: money, an index of “satisfaction,” etc. The payoff matrix is assumed
to be “symmetric,” that is the other player is looking at a payoff matrix that has the same structure.
Whereas we have previously described the Prisoner’s Dilemma only in rather imprecise terms, use of
symbols in the payoff matrix permits a formal definition that is quite generalizable. In order to qualify
technically as a Prisoner’s Dilemma, there must exist a particular set of relationships among the relative
magnitudes of payoffs a, b, c, and d in Exhibit 1.3.

Exhibit 1.1: PD Matrix Model
Your Own Behavior
Cooperate With Other
Defect

Behavior by the Other “Player”
Cooperates With You
Defects
a
c
b
d

Specifically, the payoff matrix of any PD situation must satisfy these three conditions:
1. b > a and d > c:, so that Defect is a “dominant” strategy, one which always leads to the highest payoff
no matter what behavior is expected of others.
2. a > c and b > d, so that more cooperation by the other player always increases one’s own payoff.
3. (a + a) exceeds the similar summation of the two players’ payoffs for any other outcome, so that the
cooperative solution is really “best” from the standpoint of the players.
The function of conditions 1 and 2 is probably easy to see: the former makes it advantageous for each
party to defect, and the latter makes that defection costly to the other party. Condition 3 is a bit more
subtle, and at this point its function need be indicated only briefly. Suppose that the sum of the payoffs in
a Cooperate/ Defect outcome were higher than in a Cooperate/ Cooperate, i.e., that (b + c) > (a + a).
Assume, then, that a proposed “deal” involves one player being randomly selected to cooperate and the
other to defect. Why might this proposed deal be regarded as possibly superior to a Cooperate/Cooperate
solution? (If you don’t see at least intuitively why, return to this question after the treatment of “expected
values” in Chapter II below.) In short, condition 3 is there merely to avoid the possibility that Cooperate/
Cooperate is not really the desired solution.


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In addition, some social scientists attribute a behavioral significance to the within-column payoff
variations (b - a) and (d - c). These are termed “temptation differentials” since they show the incentive to
profit by abandoning a cooperative mode of behavior. The larger these are, the less cooperation is
predicted, ceteris paribus. Similarly, the diagonal difference (a - d) is called the “cooperation differential”
since it is an index of the incentive to achieve the cooperative solution.
2. ANOTHER IMPORTANT, CLOSELY RELATED GAME: “CHICKEN”

One use of the formal PD definition just derived is to distinguish the Prisoner’s Dilemma from other
similar “dilemma”-type situations. For instance, another interesting game, called “Chicken,” can be
created by altering assumption 1 above so that if the other party is sufficiently uncooperative then cooperation becomes the optimal strategy. Specifically, assume b > a but d < c. If you were sure that the other
person were not going to cooperate, now it would actually be better to cooperate than to remain noncooperative. Since the other player would react similarly if convinced that you would not cooperate, the circumstances are such that it pays to convince the other party of one’s stubbornness and obduracy. Note
that b is the highest payoff achievable (you defect, other cooperates). This can be gained by successfully
bluffing your opponent.
As will become apparent in subsequent sections, bluffing problems are frequently involved in situations
of interest to lawyers and that is why Chicken is an important concept. A Chicken Game will be exemplified later in this chapter in the form of the Road Problem, dealing with negotiating agreement on road
repair levels. After reflecting on the Road Problem in its purely verbal form, it will be profitable to fit the
words into the sort of formal matrix model just laid out. With that forewarning about the role of the
Chicken model, we shall develop some additional terminology and then turn to the factual scenario.
3. OTHER USEFUL JARGON: “EXTERNALITIES”
The Prisoner’s Dilemma has been chosen as a starting point for several reasons. One is that--as will
become clearer and clearer as the applications multiply--the situation is an interesting one per se; it has a
more or less direct bearing on many interesting legal phenomena. A second reason, however, is that it
helps to edge one into a whole set of terminology that is helpful in conceptualizing and distinguishing
other situations.
A fundamental characteristic of the Prisoner’s Dilemma situation is the presence of some act whose
benefits exceed its costs (if any) for a single individual but whose aggregate costs to all affected parties
exceed its benefits. Condition 3 in the definition of the PD given above implies that this is true; since the
(a + a) aggregate payoffs to the two individuals at the Cooperate/ Cooperate solution are larger than the
summed payoffs at any other solution, then any defection from that solution necessarily involves a lesser
magnitude of gain to the defector than the magnitude of the loss imposed on the other player. In pursuing
their individual benefits, the players in the Prisoner’s Dilemma game will tend to impose on each other
what may be a very considerable amount of costs that overbalance any attendant benefits. It does not help
the situation that each individual can recognize the ultimately unsatisfactory outcome, the mutually selfdefeating nature of the behavior involved. This point deserves some emphasis. It is a simple but dismayingly common error to believe that the reciprocal nature of the damaging behavior either “cancels out,”
and can therefore be neglected, or that their own recognition of the reciprocity of the damages will cause
the “players” to desist from the behavior.
The Prisoner’s Dilemma anecdote sets the stage for some additional concepts dealing with costs and
benefits. Specifically, there are several economic terms of art worth introducing at this point, both

because they are useful in further articulating the Prisoner’s Dilemma type of problem and also because
they have important applications in other contexts. The terms in question deal with what economists call
“externalities.”


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Economists classify the effects of any act as being “internal” to the extent that they are felt only by the
actor and “external” to the extent that they affect third parties. Hence, the Prisoner’s Dilemma falls in a
class of situations where the internal benefits selfishly pursued by any individual are exceeded by the
external costs imposed by others engaged in similar activity. The regulation of many types of external
effects, both costs and benefits, will turn out to be a very pervasive theme in Law and Economics problems. Unfortunately, a variety of terminology is sometimes used to describe external effects. Sometimes
they are referred to simply as “externalities” or “spillover” effects. Also, the words “private” and “social”
are substituted for internal and external, respectively. These alternative sets of terminology are essentially
interchangeable. The key question involved is whether the impact of an act is confined to the person who
performs it and, if not, whether others are affected beneficially or detrimentally.
The Prisoner’s Dilemma illustrates a situation where the external effect is a cost, a harmful effect. Consider what happens to the “other” prisoner if one prisoner decides to testify rather than remain silent: the
second prisoner suffers an increase in the years that he will spend in jail. Thus, the testifying creates an
internal benefit for the prisoner who squeals, but it levies an external cost on the second prisoner. The
exact magnitude of the external cost depends on whether the second prisoner is already cooperating with
the prosecution or not.
There is a rule of thumb about external effects that is worth remembering: activities that produce external costs tend to generate the perception of a “problem” involving “too much” of the activity in question.
The PD game, of course, is a classical illustration of the imposition of heavy external costs because of (as
viewed by the prisoners) “too much” testifying. We shall shortly be dealing with problems caused when
the external effect is a benefit rather than a cost. Such a situation is generally regarded as producing a
problem of exactly the opposite sort: a tendency for there to be “too little” of the activity that produces the

external benefit.
QUESTIONS
1. Under the facts of the original PD scenario presented above, what are these magnitudes of external
cost that the prisoners impose on one another? What are the associated internal benefits to the prisoner who squeals? (Answer as specifically as possible, e.g., in terms of years or some other quantity.)
2. Suppose that a prisoner who squealed were penalized by having to serve additional time equal to the
external costs imposed on the other prisoner. What would the outcome be in terms of the amount of
cooperation with the prosecution that you would then expect?
3. Now suppose that a prisoner had to compensate the other for any external costs suffered, but that the
compensation could be in the form of a monetary payment. (This would be the equivalent of treating
the squealing as a tort.) Would either prisoner testify? Indicate any additional factual assumptions
necessary to answer this question. [Hint: Do we have to know anything about the money value of
years of freedom to each prisoner?]
4. One of the first applications of the Prisoner’s Dilemma model in the economic literature was in relation to the decisions of property owners whether or not to invest in maintenance and improvements.
See Davis and Whinston, “Economics of Urban Renewal,” 26 J.Law and Contemp.Prob. 105 (1961).
Do such activities produce “externalities”? What would you guess was the structure and content of
the PD matrix used by Davis and Whinston? Why would they apply this model to explain such
things as building codes and “urban renewal” through government acquisition and redevelopment of
large tracts?
4. ETHICAL AND OTHER EXTRALEGAL BEHAVIORAL REGULATIONS
The simple game-theoretic notions introduced above obviously provide one possible rationale for the
coercive function of a legal system in removing individuals from predictably mutually-destructive


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13

“dilemmas.” The role of “liability” or punishment in channeling behavior will be an important theme in

much of the analysis below. One should not, however, suppose that extralegal institutions have an unimportant role in the social problems addressed by laws. Extralegal behavioral influences may supplement
law in important ways or even obviate its need entirely. On the other hand, the breakdown of extralegal
pressures may supply the impetus for creation of new or modified legal rules.
This general subject is, for instance, dealt with by ethician J.L. Mackie in terms of exactly the gametheoretic methodology introduced above. He analyzes the following anecdote as a variant of the Prisoners’ Dilemma. [Ethics: Inventing Right and Wrong, 115-121 (1977).] Tom and Dan are soldiers assigned
to adjacent fortified posts in the path of an enemy attack. If both remain at these posts, they have a reasonable chance of holding out until a relief column arrives, and so of both surviving. If they both desert
their posts, the enemy will break through immediately and the chance of either of them surviving is markedly reduced. On the other hand, if one stays at his post while the other flees, the coward will have a
much better chance of survival than if both soldiers remain. In this latter case, the one who stays will have
a worse chance of survival than if they both deserted their posts.
Under the circumstances, it would be rational for both men to agree to be literally chained to their
posts. Each soldier would benefit from this loss of his own freedom of choice, provided that his comrade’s freedom was similarly constrained. An effective alternative would be some external discipline that
confronted a deserter with the prospect of a sufficiently severe punishment, such as execution. But
Mackie stresses that there can be psychological substitutes for physical chains and external penalties.
Military traditions of honor and loyalty to comrades can serve as invisible chains, while the stigma of
cowardice, with its attendant disgrace and shame, can substitute for external sanctions. Indeed, given the
hypothetical situation, one would actually prefer to belong to a group whose members were encumbered
with an appropriate set of psychological fetters.
Mackie also points out that if Tom and Dan have a general tradition of keeping agreements, they will be
able to pledge that each will persevere at his post, and the agreement-keeping tradition will then tend to
hold each man there. In practice, however, a general agreement-keeping tradition is likely to be rather less
effective in situations of extreme stress (such as our hypothetical one) than more focused, situation-specific mechanisms as exemplified by military traditions of honor and loyalty. On the other hand, a general
ethic of agreement-keeping has the advantage of being more flexible and widely applicable than specialpurpose ethical constraints. A tradition of observing agreements can support the making and keeping of
all sorts of useful bargains. Thus, observes Mackie, Hume was quite right in saying that a man is the more
useful, both to himself and to others, the greater degree of probity and honor he is endowed with.
The particular example used to illustrate this form of two-person game is both dramatic and realistic,
but it has the disadvantage that it does not lend itself to repeated trials by the same two players. That is, it
deals with a single-trial game rather than an “iterated” one. Hence, Mackie considers another example
where even if Tom, say, comes off badly at the first trial he will still survive to play with Dan again. The
following assumptions are made: (1) that each man has only a weak agreement-keeping tendency; (2) that
neither can see, on any one occasion, whether the other is keeping the bargain until he himself is committed either to keeping it or to breaking it; (3) that if both men keep the agreement on one occasion, each
is more likely to keep it next time, whereas if either or both men break the agreement on one occasion,

each is less likely to keep it next time; (4) that all these tendencies are known to both men; and (5) that
each time Tom and Dan play this game they know that they will have to play it again with one another.
These assumptions are said to alter the form of the game in the following way:
[I]f, on any one occasion, Dan is going to keep the agreement, it will be to Tom’s selfish
advantage, with a view to the future, to do so too, though if Dan is going to break the agreement this
time, it will be to Tom’s advantage to break it. And of course the situation is still symmetrical. Selfinterest no longer unambiguously urges each man to break the agreement on any one occasion:


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Chapter 1

consequently only a fairly weak agreement-keeping tendency will be needed to tip the balance. Fairly
obvious and natural assumptions lead to a similar conclusion if we extend the game in another
direction as well, and assume that there are more than two players.7
Mackie also considers the possibility of outcomes that are not symmetrical for the parties involved:
Even if Tom and Dan are initially placed alike, there may be several possible agreements between
them, each of which is better for each man singly than the results of failure to agree or of failure to
keep the agreement, but some of which are in various degrees more advantageous to Tom than to
Dan, and vice versa. In these circumstances the man who is, or gives the appearance of being, the
more reluctant to make, or to adhere to, an agreement is likely to get more advantageous terms.
Though complete intransigence in either party is disastrous for both, incomplete relative intransigence is differentially advantageous to its possessor. This holds, as I have said, even if the initial
situation is symmetrical; but if one party has less to lose by failure to agree, or less to gain from a
stable agreement, further possibilities of unequal agreements arise.8
Finally, the conclusion of this ethician’s section on “Game Theory” provides an appropriate combination both of endorsement of the game-theoretic conceptualization and of caveat about the limitations of
any general model:
There can be no doubt that many real-life situations contain, as at least part of their causally relevant structure, patterns of relationship of which various simple ‘games’ are an illuminating description. An international arms race is one obvious example: another is the situation where inflation can
be slowed down only if different trade unions can agree to limit their demands for wage increases.

One merit of such simplified analyses is that they show dramatically how the combined outcome of
several intentional actions, even of well-informed and rational agents, may be something that no one
of the agents involved has intended or would intend. * * * The main moral is the practical value of
the notion of obligation, of an invisible and indeed fictitious tie or bond, whether this takes the form
of a general requirement to keep whatever agreements one makes or of various specific duties like
those of military honour or of loyalty to comrades or to an organization.
* * * The real weakness of the Hobbesian solution lies not in anything that the game theory models show, but in what, just by being models, they leave out. Real situations always incorporate, along
with the skeletal structure of some fairly simple game, other forces and tendencies whose strength
varies through time.9
QUESTIONS
5. Provide an illustration of a situation wherein an ethical, moral or other extralegal compulsion seems
adequately to regulate a form of behavior that might otherwise necessitate some more formal sanction system. Exemplify, if possible, a situation wherein the progressive breakdown of a formerly
effective extralegal behavioral convention has already caused, or seems likely to cause, recourse to a
formal coercive regulation.
6. Exactly how does a factor such as “guilt” or “approbation” change the PD matrices? What changes in
the facts of the original PD scenario in the text above would make it plausible that these factors
would eliminate the dilemma for the prisoners?
7. What circumstances determine whether extralegal rules are preferable to formal legal sanctions? Are
the most relevant considerations on the “cost” side or the “benefit” side? Are relative “flexibility”
advantages of interest?
7

J.L. Mackie, Ethics: Inventing Right and Wrong, (1977) at 118.
Ibid., 118-19.
9
Ibid., 120.
8


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ANALYZING CHOICE UNDER ALTERNATIVE RULES

15

8. Even though there are fines for traffic infractions and legal liabilities imposed for driving-related
torts, there is arguably a certain gaming aspect to careful driving, an activity that produces “external
benefits.” This exchange in F. Scott Fitzgerald’s The Great Gatsby is instructive:
“You’re a rotten driver,” I protested. “Either you ought to be more careful or you oughtn’t to
drive at all.”
“I am careful.”
“No, you’re not.”
“Well, other people are,” she said lightly.
“What’s that got to do with it?”
“They’ll keep out of my way,” she insisted. “It takes two to make an accident.”
“Suppose you met somebody just as careless as yourself.”
“I hope I never will,” she answered. “I hate careless people. That’s why I like you.”
In your experience, do informal codes of “driving courtesy” differ substantially as one travels from
place to place? If so, how and why? Would you expect their degree of observance or “strength” to vary
predictably in accordance with any particular circumstances?
5. Re-read and critique the paragraph quoted above on the iterated game as played under Mackie’s
five assumptions. What is your own analysis of the difference it makes if the game is an iterated one
rather than a single-play game?
6. Suppose that a Prisoners Dilemma game is to be played in iterated form, but the number of trials is
known to be equal to n, where n is any positive number. What can you say about the results of this
game?10
7. Do you understand the paragraph quoted in the text above that deals with asymmetrical results and
the advantages of intransigence? If you do not understand it, return to this question after completing the
“Road Problem” in the next section below.
5. EXTERNAL BENEFITS, EXCLUDABILITY AND “FREE RIDERS”

As indicated earlier, external effects may be produced in the form of benefits rather than the harms
exemplified in the original Prisoner’s Dilemma situation. We turn now to a specific consideration of such
external benefit production. The “road problem” scenario provided below deals with external benefits and
the difficulties that occur when such benefits are potentially available at no cost. In the original Prisoner’s
Dilemma presented above, it is at least arguable that the prisoners “should” be kept in their dilemma.
Indeed, one function of Law may be to keep certain types of people in a dilemma-like environment
because, although this is detrimental to the “prisoners,” it is regarded as producing benefits to other parts
of society. By contrast, in the road scenario below, the sympathy or normative feeling that one has for the
players will be less ambiguous; most people would agree that the situation is somehow troubling and that
the “players” should be removed from the dilemma if possible.

10

Although logic may seem to suggest that repeated plays of the same game should not produce any change in
behavior, a number of game theorists argue that altered behavior will in fact occur. See, e.g., R. Luce & H. Raiffa,
Games and Decisions, at 102-04. A stronger case for unaltered behavior can be made when the number of iterations
(the value n in the text) is known. The nth iteration becomes, in effect, a non-iterated game and the non-cooperative
strategy is therefore clearly dominant. But, it is reasoned, if this is known, then there is no reason to cooperate on the
(n-l)th play. A similar logic can then, of course, be extended backward without limit.