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 Akerlof Linda Babcock
Sendhil Mullainathan Matthew Rabin
Peter Diamond Jon Elster
Eldar Shafir Robert Shiller
Ernst Fehr Daniel Kahneman
Cass Sunstein Richard Thaler
Behavioral Game Theory Experiments in Strategic Interaction
Colin F. Camerer
Russell Sage Foundation, New York, New York Princeton University Press, Princeton, New Jersey
41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 3 Market Place, Woodstock, Oxfordshire OX20 1SY and Russell Sage Foundation, 112 East 64th Street, New York, New York 10021 All Rights Reserved 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 330 .01 5193—dc21 British Library Cataloging-in-Publication Data is available This book was composed in ITC New Baskerville with ZzTEX by Princeton Editorial Associates, Inc., Scottsdale, Arizona Printed on acid-free paper. www.pup.princeton.edu www.russellsage.org Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
To my parents
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
1 5 7 8 12 16 20 24 25 25 34
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 vii
43 48 59 59 60 62 63 64 65 65 65 67 68
Contents 2.5 2.6
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
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
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
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
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
408 411 427 427 430 436 439 445 446 453 458 462
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
465 466 466 468 469 469 469 470 471 473
Appendix: Design Details
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
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.
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
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
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.
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.
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.
Schotter and Sopher (2000).
What Is Game Theory Good For?
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.
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
Raiffa pointed this out many times, calling game theory “asymmetrically normative.”