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Behavioral game theory experiments in strategic interaction


Behavioral Game Theory


The Roundtable Series in Behavioral Economics
The Roundtable Series in Behavioral Economics aims to advance research
in the new interdisciplinary field of behavioral economics. Behavioral economics uses facts, models, and methods from neighboring sciences to establish descriptively accurate findings about human cognitive ability and social
interaction and to explore the implications of these findings for economic
behavior. The most fertile neighboring science in recent decades has been
psychology, but sociology, anthropology, biology, and other fields can usefully influence economics as well. The Roundtable Series publishes books in
economics that are deeply rooted in empirical findings or methods from one
or more neighboring sciences and advance economics on its own terms—
generating theoretical insights, making more accurate predictions of field
phenomena, and suggesting better policy.
Colin Camerer and Ernst Fehr, Series Editors

The Behavioral Economics Roundtable
Henry Aaron

George Loewenstein


George Akerlof
Linda Babcock

Sendhil Mullainathan
Matthew Rabin

Colin Camerer

Thomas Schelling

Peter Diamond
Jon Elster

Eldar Shafir
Robert Shiller

Ernst Fehr
Daniel Kahneman

Cass Sunstein
Richard Thaler

David Laibson

Richard Zeckhauser


Behavioral Game Theory
Experiments in Strategic Interaction

Colin F. Camerer

Russell Sage Foundation, New York, New York
Princeton University Press, Princeton, New Jersey


Copyright © 2003 by Russell Sage Foundation
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Library of Congress Cataloging-in-Publication Data
Camerer, Colin, 1959–
Behavioral game theory : experiments in strategic interaction / Colin F. Camerer.
p. cm.
Includes bibliographic references and index.
ISBN 0-691-09039-4 (alk. paper)
1. Game theory. 2. Statistical decisions. 3. Negotiation—Mathematical
models. 4. Decision making. I. Title. II. Series.
HB144 .C364 2003
2002034642
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10 9 8 7 6 5 4 3 2 1


To my parents



Contents

Preface

xiii

1 Introduction
1.1
What Is Game Theory Good For?
1.2
Three Examples
1.2.1 Example 1: Ultimatum Bargaining
1.2.2 Example 2: Path-Dependent Coordination in
“Continental Divide” Games
1.2.3 Example 3: “Beauty Contests” and Iterated
Dominance
1.3
Experimental Regularity and Behavioral Game Theory
1.4
Conclusion
Appendix
A1.1 Basic Game Theory
A1.2 Experimental Design

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2 Dictator, Ultimatum, and Trust Games
2.1
Ultimatum and Dictator Games: Basic Results
2.2
Methodological Variables
2.2.1 Repetition
2.2.2 Methodology: Stakes
2.2.3 Anonymity and Experimenter “Blindness”
2.3
Demographic Variables
2.3.1 Gender
2.3.2 Race
2.3.3 Academic Major
2.3.4 Age
2.3.5 Brains, Biology, and Beauty
2.4
Culture
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viii

Contents
2.5
2.6

2.7

2.8

2.9

Descriptive Variables: Labeling and Context
Structural Variables
2.6.1 Identity, Communication, and Entitlement
2.6.2 Competitive Pressure and Outside Options
2.6.3 Information about the Amount Being Divided
2.6.4 Multiperson Games
2.6.5 Intentions: Influence of Unchosen Alternatives
Trust Games
2.7.1 Is Trustworthiness Just Altruism?
2.7.2 Indirect Reciprocity, Karma, Culture
2.7.3 A Complex Omnibus Game
2.7.4 Multistage Trust Games
2.7.5 Gift Exchange in Experimental Labor Markets
Theory
2.8.1 Pure and Impure Altruism
2.8.2 Inequality-Aversion Theories
2.8.3 Fairness Equilibrium (Rabin)
2.8.4 Extensive-Form Fairness Equilibrium
2.8.5 Comparing Approaches
Conclusion

3 Mixed-Strategy Equilibrium
3.1
Early Studies
3.2
Modern Studies
3.3
Subjective Randomization and Mixed Strategies
3.4
Explicit Randomization
3.5
Patent Race and Location Games with Mixed Equilibria
3.6
Two Field Studies
3.7
Conclusion

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4 Bargaining
151
4.1
Unstructured Bargaining
153
4.1.1 Unstructured Bargaining over Ticket Allocations
153
4.1.2 Self-Serving Interpretations of Evidence in
Unstructured Bargaining
158
4.2
Structured Bargaining
161
4.2.1 Finite Alternating-Offer Games
161
4.2.2 Limited Computation
167
4.2.3 Random Termination
174
4.2.4 Games with Fixed Delay Costs and Outside Options 175
4.3
Bargaining under Incomplete Information
182
4.3.1 One-Sided Buyer Information with
Seller-Only Offers
183


ix

Contents

4.4

4.3.2 One-Sided Private Information and Strikes
4.3.3 Sealed-Bid Mechanisms for Bilateral Bargaining
Conclusion

5 Dominance-Solvable Games
5.1
Simple Dominance-Solvable Games
5.1.1 Games Solvable by Two Steps of Iterated
Dominance
5.1.2 Iterated Dominance and Tree-Matrix Differences
5.1.3 A Partially Dominance-Solvable Patent Race Game
5.2
Beauty Contest Games
5.3
Games in Which Iterated Reasoning Decreases Payoffs
5.3.1 Centipede Games
5.3.2 Prisoners’ Dilemma and Quasi-Centipede Games
5.3.3 Price Competition
5.3.4 The Travelers’ Dilemma
5.3.5 The “Email Game”
5.3.6 An Implementation Mechanism That Uses
Iterated Dominance
5.4
When More Iteration Is Better: The “Dirty Faces” Game
5.5
The “Groucho Marx” Theorem in Zero-Sum
Betting
5.6
Structural Models of Decision Rules and Levels of
Reasoning
5.7
Theories
5.7.1 Multiple Types
5.7.2 Payoff-Sensitive Noisy Iteration
5.7.3 QRE Refinements: Differences and Asymmetry
in λ
5.7.4 A Poisson Cognitive Hierarchy
5.8
Conclusion
Appendix: Raw Choices in Email Game and
Additional Data
6 Learning
6.1
Theories of Learning
6.2
Reinforcement Learning
6.2.1 Reinforcement in Weak-Link Games
6.2.2 Reinforcement with Payoff Variability
6.2.3 Reinforcement with “Mood Shocks”
6.2.4 Information Conditions
6.3
Belief Learning
6.3.1 Weighted Fictitious Play

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x

Contents

6.4
6.5

6.6

6.7
6.8
6.9

6.3.2 General Belief Learning
6.3.3 Learning Direction Theory
6.3.4 Bayesian Learning
6.3.5 Measuring Beliefs Directly
6.3.6 Population-Level Replicator Dynamics
Imitation Learning
Comparative Studies
6.5.1 Comparing Belief Models
6.5.2 Comparing Belief and Reinforcement Models
Experience-Weighted Attraction (EWA) Learning
6.6.1 Example: Continental Divide
6.6.2 Example: p-Beauty Contest, and Sophistication
6.6.3 Functional EWA (fEWA)
Rule Learning
Econometric Studies of Estimation Properties
Conclusions

7 Coordination
7.1
Matching Games
7.1.1 Assignment Games and Visual Selection
7.1.2 Unpacking Focality
7.2
Asymmetric Players: Battle of the Sexes
7.2.1 Outside Options
7.2.2 Communication
7.2.3 Evolution of Meaning
7.2.4 External Assignment
7.2.5 Timing
7.3
Market Entry Games
7.3.1 Multiple Markets
7.3.2 Skill
7.4
Payoff-Asymmetric Order-Statistic Games
7.4.1 Experimental Evidence
7.4.2 Weak-Link Games
7.4.3 Mergers, Bonus Announcements, and
“Leadership”
7.4.4 Median-Action Games
7.4.5 Preplay Auctions and Entry Fees
7.4.6 General Order-Statistic Games
7.5
Selecting Selection Principles
7.5.1 Simplicity
7.5.2 Empirical Comparison of Selection Principles

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xi

Contents
7.6

7.7

Applications: Path-Dependence, Market Adoption, and
Corporate Culture
7.6.1 Path-Dependence: Creating a Laboratory
“Continental Divide”
7.6.2 Market Adoption
7.6.3 Culture
Conclusion
Appendix: Psycholinguistics

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405

8 Signaling and Reputation
8.1
Simple Signaling Games and Adaptive Dynamics
8.2
Specialized Signaling Games
8.2.1 Lobbying
8.2.2 Corporate Finance
8.2.3 Games with Ratchet Effects
8.2.4 Belief Learning in Limit Pricing Signaling Games
8.3
Reputation Formation
8.3.1 Trust
8.3.2 Entry Deterrence
8.3.3 Learning in Repeated Games
8.4
Conclusion

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462

9 Conclusion: What Do We Know, and Where Do We Go?
9.1
Summary of Results
9.1.1 Simple Bargaining Games
9.1.2 Mixed-Strategy Equilibria
9.1.3 Bargaining
9.1.4 Iterated Dominance
9.1.5 Learning
9.1.6 Coordination
9.1.7 Signaling
9.2
Top Ten Open Research Questions

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Appendix: Design Details

477

References

497

Index

535



Preface

IN ECONOMICS AT THE UNIVERSITY OF CHICAGO in the late 1970s, game theory was considered a messy analytical swamp between monopoly and perfect
competition. My intermediate price theory teacher explained cynically how
von Neumann and Morgenstern had both solved one problem that was no
longer a problem (by giving a method to measure utilities, which was not
needed after the ordinal revolution) and failed to solve the hard problem
(uniqueness of equilibrium in all games). In class we therefore stuck to the
important polar cases and hoped that two firms would be perfectly competitive, so we didn’t need game theory. Fortunately, my first job in 1981 (a de
facto postdoc) was up the road at Northwestern which had an unbelievable
all-star team of game theorists in its MEDS Department—Bengt Holmstrom,
Ehud Kalai, Paul Milgrom, Roger Myerson, John Roberts, Mark Satterthwaite. You couldn’t help but learn some game theory, and get excited about
it, just breathing the air in seminars. But my background in cognitive psychology and behavioral decision research also made it natural to look at
games and ask how people with cognitive limits and emotions—i.e., normal
people—would behave.
So the roots of this book go back at least that far. A conference organized
to honor Hilly Einhorn, who died tragically young, gave me a chance to
put ideas on paper (published in 1990) and coin the term “behavioral
game theory” for the empirical, descriptive approach rooted in data and
psychological fact.
People who have influenced me intellectually (in loosely chronological
order) include my thesis advisors, Hilly and Robin Hogarth, Charlie Plott
(who taught a Ph.D. course at Chicago in 1980 which changed the course of
my research), Ken MacCrimmon, Howard Kunreuther, Daniel Kahneman,
Paul Slovic, Amos Tversky, John Kagel, George Loewenstein, Jon Baron, Eric
Johnson, Dick Thaler, Matthew Rabin, Marc Knez, Teck Ho, Kuan Chong,
and my students and many other collaborators.
xiii


xiv

Preface

This book has been a long time in the making, and it has benefited from
ideas of many people. It was supported by a wonderful year at the Center
for Advanced Study in the Behavioral Sciences in 1997–98. (Is it possible to
have a bad year there? It poured rain the whole time and it was still fun.)
Hundreds of seminar participants, and my colleagues in the MacArthur
Norms and Preferences Network, have shaped my thinking over the years.
Students in my Psychology 101 class at Caltech, colleagues Bruno Broseta,
Miguel Costa-Gomes, John Kennan, Roberto Weber, and in particular Vince
Crawford, and three anonymous referees all commented helpfully on the
manuscript. Research assistants Chris Anderson, Dan Clendenning, Ming
Hsu, and Angela Hung helped with graphics and editorial support. Gail
Nash, Rachel Kibble, and especially the tireless Karen Kerbs did amazing
work on the manuscript with great aplomb. Thanks also to Peter Dougherty
of Princeton University Press for unflagging cheerleading, sage advice at
all the right moments, and some cool free books. Timely moral support
was provided throughout by Peter, and by a fortune cookie from the local
Chinese delivery place. Their message arrived just before I finished the
tedious process of reviewing the copyediting. It said—no lie—“You are soon
to achieve perfection.”
The book is written so that the reader can either “dive” or “snorkel.”
Snorkeling means swimming along the surface, looking at the pretty fish but
not going so deep that you need special equipment (e.g., intimate knowledge of game theory) to breathe. Snorkelers should appreciate highlights
of crucial facts about what has been learned from experiments relative to
theory, and how those findings suggest new theory (summarized in section
summaries). Divers will want to explore the details of studies and make their
own judgments about what was learned and important.
I have also skimped on, or omitted, extremely important areas because
they are either well covered elsewhere or simply overwhelming—especially
experiments on cooperative games, unstructured bargaining (see Roth,
1995b, for more on this subject), public goods and prisoners’ dilemma
games, and auctions (see Kagel, 1995, or Kagel and Levin, in press).
I have followed certain writing conventions. My goal is to convey the
regularities that have been discovered in experimental studies of game
theory, and a feeling for the care, craftsmanship, and conventions of the
experimental method. Some studies have been overemphasized and some
deemphasized. My preference is to describe the first or last studies and
the most solid or interesting results. In summarizing results, the goal is
full disclosure without clutter and irrelevance. If you are curious about a
detail of the experiments or data that have not been reported, they probably
were omitted because they do not matter (or were omitted in the original
published reporting); however, I would be horrified if you took this as
an excuse to forgo looking at the original article if you are really curious.


Preface

xv

For example, when the data from various periods of an experiment are
lumped together and reported as an average, that usually means there is
no interesting learning across periods.
Details of how experiments are conducted (e.g., matching protocol,
incentive levels) have been collected in the appendix at the end of the book
to keep you from being distracted as you read.
Interested in teaching from this book? Start with Chapter 1 (duh) and
have the students actually play the three games in that chapter to get a feel
for what piques their curiosity. Pick and choose other material to suit the
interests and technical mastery of the students. Chapters 2 and 7 will be of
broadest interest to noneconomists, Chapter 6 is heavy on econometrics,
and Chapter 8 (and parts of Chapter 4) is the most technically demanding.



Behavioral Game Theory



1

Introduction

GAME THEORY IS ABOUT WHAT HAPPENS when people—or genes, or nations—
interact. Here are some examples: Tennis players deciding whether to serve
to the left or right side of the court; the only bakery in town offering a discounted price on pastries just before it closes; employees deciding how hard
to work when the boss is away; an Arab rug seller deciding how quickly to
lower his price when haggling with a tourist; rival drug firms investing in a
race to reach patent; an e-commerce auction company learning which features to add to its website by trial and error; real estate developers guessing
when a downtrodden urban neighborhood will spring back to life; San Francisco commuters deciding which route to work will be quickest when the Bay
Bridge is closed; Lamelara men in Indonesia deciding whether to join the
day’s whale hunt, and how to divide the whale if they catch one; airline
workers hustling to get a plane away from the gate on time; MBAs deciding what their degree will signal to prospective employers (and whether
quitting after the first year of their two-year program to join a dot-com
startup signals guts or stupidity); a man framing a memento from when
he first met his wife, as a gift on their first official date a year later (they’re
happily married now!); and people bidding for art or oil leases, or for knickknacks on eBay. These examples illustrate, respectively, ultimatum games
(bakery, Chapter 2), gift exchange (employees, Chapter 2), mixed equilibrium (tennis, Chapter 3), Tunisian bazaar bargaining (rug seller, Chapter
4), patent race games (patents, Chapter 5), learning (e-commerce, Chapter 6), stag hunt games (whalers, Chapter 7), weak-link games (airlines,
Chapter 7), order-statistic games (developers, Chapter 7), signaling (MBAs
and romance, Chapter 8), auctions (bidding, Chapter 9).
1


2

1

Introduction

In all of these situations, a person (or firm) must anticipate what others will do and what others will infer from the person’s own actions. A
game is a mathematical x-ray of the crucial features of these situations.
A game consists of the “strategies” each of several “players” have, with precise rules for the order in which players choose strategies, the information
they have when they choose, and how they rate the desirability (or “utility”) of resulting outcomes. An appendix to this chapter describes the basic
mathematics of game theory and gives some references for further reading.
Game theory has a very clear paternity. Many of its main features were
introduced by von Neumann and Morgenstern in 1944 (following earlier
work in the 1920s by von Neumann, Borel, and Zermelo). A few years later,
John Nash proposed a “solution” to the problem of how rational players
would play, now called Nash equilibrium. Nash’s idea, based on the idea of
equilibrium in a physical system, was that players would adjust their strategies
until no player could benefit from changing. All players are then choosing
strategies that are best (utility-maximizing) responses to all the other players’
strategies. Important steps in the 1960s were the realization that behavior
in repeated sequences of one-shot games could differ substantially from
behavior in one-shot games, and theories in which a player can have private
information about her values (or “type”), provided all players know the
probabilities of what those types might be. In 1994, Nash, John Harsanyi,
and Reinhard Selten (an active experimenter) shared the Nobel Prize in
Economic Science for their pathbreaking contributions.
In the past fifty years, game theory has gradually become a standard
language in economics and is increasingly used in other social sciences (and
in biology). In economics, game theory is used to analyze behavior of firms
that worry about what their competitors will do.1 Game theory is also good
for understanding how workers behave in firms (such as the reaction of
CEOs or salespeople to incentive contracts), the spread of social conventions
such as language and fashion, and which genes or cultural practices will
spread.
The power of game theory is its generality and mathematical precision.
The same basic ideas are used to analyze all the games—tennis, bargaining
for rugs, romance, whale-hunting—described in the first paragraph of this
chapter. Game theory is also boldly precise. Suppose an Arab rug seller
can always buy more rugs cheaply, an interested tourist values the rugs at
somewhere between $10 and $1000, and the seller has a good idea of how
1 Game theory fills the conceptual gap between a single monopoly, which need not worry about what
other firms and consumers will do because it has monopoly power, and “perfect competition,” in which
no firm is big enough for competitors to worry about. Game theory is used to study the intermediate case,
“oligopoly,” in which there are few enough firms that each company should anticipate what the others
will do.


1 Introduction

3

impatient the tourist is but isn’t sure how much the tourist likes a particular
rug. Then game theory tells you exactly what price the seller should start out
at, and exactly how quickly he should cut the price as the tourist hems and
haws. In experimental re-creations of this kind of rug-selling, the theory is
half-right and half-wrong: it’s wrong about the opening prices sellers state,
but the rate at which experimental sellers drop their prices over time is
amazingly close to the rate that game theory predicts (see Chapter 4).
It is important to distinguish games from game theory. Games are a taxonomy of strategic situations, a rough equivalent for social science of the
periodic table of elements in chemistry. Analytical game theory is a mathematical derivation of what players with different cognitive capabilities are
likely to do in games.2 Game theory is often highly mathematical (which has
limited its spread outside economics) and is usually based on introspection
and guesses rather than careful observation of how people actually play in
games. This book aims to correct the imbalance of theory and facts by describing hundreds of experiments in which people interact strategically. The
results are used to create behavioral game theory. Behavioral game theory is
about what players actually do. It expands analytical theory by adding emotion, mistakes, limited foresight, doubts about how smart others are, and
learning to analytical game theory (Colman, in press, gives a more philosophical perspective). Behavioral game theory is one branch of behavioral
economics, an approach to economics which uses psychological regularity
to suggest ways to weaken rationality assumptions and extend theory (see
Camerer and Loewenstein, 2003).
Because the language of game theory is both rich and crisp, it could
unify many parts of social science. For example, trust is studied by social
psychologists, sociologists, philosophers, economists interested in economic
development, and others. But what is trust? This slippery concept can be
precisely defined in a game: Would you lend money to somebody who
doesn’t have to pay you back, but might feel morally obliged to do so? If you
would, you trust her. If she pays you back, she is trustworthy. This definition
gives a way to measure trust, and has been used in experiments in many
places (including Bulgaria, South Africa, and Kenya; see Chapter 3).
The spread of game theory outside of economics has suffered, I believe,
from the misconception that you need to know a lot of fancy math to apply
it, and from the fact that most predictions of analytical game theory are not
well grounded in observation. The need for empirical regularity to inform

2 To be precise, this book is only about “noncooperative” game theory—that is, when players cannot make
binding agreements about what to do, so they must guess what others will do. Cooperative game theory is a
complementary branch of game theory which deals with how players divide the spoils after they have made
binding agreements.


4

1

Introduction

game theory has been recognized many times. In the opening pages of their
seminal book, von Neumann and Morgenstern (1944, p. 4) wrote:
the empirical background of economic science is definitely inadequate.
Our knowledge of the relevant facts of economics is incomparably
smaller than that commanded in physics at the time when mathematization of that subject was achieved. . . . It would have been absurd in
physics to expect Kepler and Newton without Tycho Brahe—and there
is no reason to hope for an easier development in economics.
This book is focused on experiments as empirical background. Game
theory has also been tested using data that naturally occur in field settings
(particularly in clearly structured situations such as auctions). But experimental control is particularly useful because game theory predictions often
depend sensitively on the choices players have, how they value outcomes,
what they know, the order in which they move, and so forth. As Crawford
(1997, p. 207) explains:
Behavior in games is notoriously sensitive to details of the environment,
so that strategic models carry a heavy informational burden, which is
often compounded in the field by an inability to observe all relevant
variables. Important advances in experimental technique over the past
three decades allow a control that often gives experiments a decisive
advantage in identifying the relationship between behavior and environment. . . . For many questions, [experimental data are] the most
important source of empirical information we have, and [they are] unlikely to be less reliable than casual empiricism or introspection.
Of course, it is important to ask how well the results of experiments
with (mostly) college students playing for a couple of hours for modest financial stakes generalize to workers in firms, companies creating corporate
strategy, diplomats negotiating, and so forth. But these doubts about generalizability are a demand for more elaborate experiments, not a dismissal
of the experimental method per se. Experimenters have studied a few dimensions of generalizability—particularly the effects of playing for more
money, which are usually small. But more ambitious experiments with teams
of players, complex environments, communication, and overlapping generations3 would enhance generalizability further, and people should do more
of them.

3 See

Schotter and Sopher (2000).


1.1

What Is Game Theory Good For?

5

1.1 What Is Game Theory Good For?
Is game theory meant to predict what people do, to give them advice, or
what? The theorist’s answer is that game theory is none of the above—it is
simply “analytical,” a body of answers to mathematical questions about what
players with various degrees of rationality will do. If people don’t play the
way theory says, their behavior has not proved the mathematics wrong, any
more than finding that cashiers sometimes give the wrong change disproves
arithmetic.
In practice, however, the tools of analytical game theory are used to
predict, and also to explain (or “postdict”4 ) and prescribe. Auctions are a
good example of all three uses of game theory. Based on precise assumptions
about the rules of the auction and the way in which bidders value an object,
such as an oil lease or a painting, auction theory then derives how much
rational bidders will pay.
Theory can help explain why some types of auction are more common
than others. For example, in “second-price” or Vickrey auctions the high
bidder buys the object being auctioned at a price equal to the second-highest
bid. Under some conditions these auctions should, in theory, raise more
revenue for sellers than traditional first-price auctions in which the high
bidder pays what she bid. But second-price auctions are rare (see LuckingReilly, 2000). Why? Game theory offers an explanation: Since the high
bidder pays a price other than what she bid in a second-price auction, such
auctions are vulnerable to manipulation by the seller (who can sneak in an
artificial bid to force the high bidder to pay more).
How well does auction theory predict? Tests with field data are problematic: Because bidders’ valuations are usually hidden, it is difficult to
tell whether they are bidding optimally, although some predictions can be
tested. Fortunately, there are many careful experiments (see Kagel, 1995;
Kagel and Levin, in press). The results of these experiments are mixed. In
private-value auctions in which each player has her own personal value for
the object (and doesn’t care how much others value it), people bid remarkably close to the amounts they are predicted to, even when the function
mapping values into bids is nonlinear and counterintuitive.5
In common-value auctions the value of the object is essentially the
same for everyone, but is uncertain. Bidding for leases on oil tracts is an
example—different oil companies would all value the oil in the same way
but aren’t sure how much oil is there. In these auctions players who are most
optimistic about the value of the object tend to bid the highest and win.
4 In some domains of social science, these kinds of game-theoretic “stories” about how an institution or
event unfolded are called “analytical narratives” and are proving increasingly popular (Bates et al., 1998).
5 See

Chen and Plott (1998) and the sealed-bid mechanism results in Chapter 4.


6

1

Introduction

The problem is that, if you win, it means you were much more optimistic
than any other bidder and probably paid more than the object is worth,
a possibility called the “winner’s curse.” Analytical game theory assumes
rational bidders will anticipate the winner’s curse and bid very conservatively
to avoid it. Experiments show that players do not anticipate the winner’s
curse, so winning bidders generally pay more than they should.
Perhaps the most important modern use of auction theory is to prescribe how to bid in an auction, or how to design an auction. The shining triumphs of modern auction theory are recent auctions of airwaves to
telecommunications companies. In several auctions in different countries,
regulatory agencies decided to put airwave spectrum up for auction. An auction raises government revenue and, ideally, ensures that a public resource
ends up in the hands of the firms that are best able to create value from
it. In most countries, the auctions were designed in collaborations among
theorists and experimental “testbedding” that helped detect unanticipated
weaknesses in proposed designs (like using a wind tunnel to test the design
of an airplane wing, or a “tow-tank” pool to see which ship designs sink and
which float). The designs that emerged were not exactly copied from books
on auction theory. Instead, theorists spent a lot of time pointing out how
motivated bidders could exploit loopholes in designs proposed by lawyers
and regulators, and using the results of testbedding to improve designs. Auction designers opted for a design that gave bidders a chance to learn from
potential mistakes and from watching others, rather than a simpler “sealedbid” design in which bidders simply mail in bids and the Federal Communications Commission opens the envelopes and announces the highest
ones. One of the most powerful and surprising ideas in auction theory—
“revenue equivalence”—is that some types of auctions will, in theory, raise
the same amount of revenue as other auctions that are quite different in
structure. (For example, an “English” auction, in which prices are raised
slowly until only one bidder remains, is revenue-equivalent to a sealed-bid
“Vickrey” auction, in which the highest bidder pays what the second-highest
bidder bid.) But when it came to designing an auction that actual companies would participate in with billions of dollars on the line, the auction
designers were not willing to bet that behavior would actually be equivalent
in different types of auctions, despite what theory predicted. Their design
choices reflect an implicit theory of actual behavior in games that is probably
closer to the ideas in this book than to standard theory based on unlimited
mutual rationality. Notice that, in this process of design and prescription,
guessing accurately how players will actually behave—good prediction—is
crucial.6

6 Howard

Raiffa pointed this out many times, calling game theory “asymmetrically normative.”


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