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This interview with Eric Maskin by Edward Tenner was prepared for

the January 2, 2002 edition of U.S.

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Insights of a Beautiful Mind

In the movie, "A Beautiful Mind," Princeton

graduate student John Nash gets the inspiration that will win him

the Nobel prize when he persuades his three buddies not to compete

for the same knockout blonde. They spot the buxom blonde standing

with four other women in a Princeton bar. Nash cautions against all

of them going for the blonde, on the theory that, by competing, none

would get her, and none would get any girl that night, because the

others would know they were second choice.

So the four men pursue the ordinary-looking women and ignore the

blonde.

She is dumbfounded. On his way out, Nash turns and says "Thank

you" to the blonde. According to the screenwriter, the light bulb

has flashed inside Nash’s brain, and Nash has had an inspiration about

"game theory," the way mathematicians describe situations

in which people have to worry about what other people are going to

do.

The anecdote is hokum, of course, and much of the movie embellishes,

even fictionalizes, the facts. The truth can be found in Nash’s

biography,

"A Beautiful Mind," written by Sylvia Nasar, and "The

Essential John Nash," an annotated anthology edited by Harold

W. Kuhn and Sylvia Nasar (Princeton University Press, $29.95).

Nash received his bachelor’s and master’s degrees from Carnegie

Institute

of Technology, and when he received his Ph.D. from Princeton

University

he was just 21 years old. He taught at Princeton, New York University,

and Massachusetts Institute of Technology. He worked at several

research

institutions including the Institute for Advanced Study, Rand

Corporation,

and Courant Institute. Although Nash had national security clearance

for a time, he never really worked in the code-breaking field of

mathematics

that is featured in the movie.

Because of mental illness he dropped out of sight in 1959 and was

virtually unknown outside of the academic community until he received

the Nobel Prize for Economics in 1994 for game theory. His prize was

for introducing the distinction between cooperative games (in which

binding agreements can be made) and non-cooperative games, (where

binding agreements are not feasible). Nash proposed a way to predict

what will happen in a situation where one person’s gain is not the

second person’s loss, a concept that later came to be called the

"Nash

equilibrium."

But why is game theory so valuable that the British

government called in game theory experts for its high-stakes mobile

phone line auction? We asked a Princeton University historian, Edward

Tenner, to discuss Nash’s work with an Institute for Advanced Study

scholar, Eric S. Maskin.

Eric Maskin, the Albert O. Hirschman Professor in the

School of Social Science at the Institute, is an economic theorist

with wide-ranging interests, including game theory, the economics

of incentives, and social choice theory, Among his current projects

is a comparison of electoral rules such as majority voting,

understanding

the role of monetary policy, and studying the advantages and drawbacks

of protecting intellectual property.

A fellow of the American Academy of Arts and Sciences, Maskin majored

in mathematics at Harvard University, Class of 1972. He has master’s

and Ph.D. degrees in applied mathematics from Harvard and an honorary

master’s from Cambridge University. He taught at the MIT and Harvard

before joining the faculty of the Institute for Advanced Study in

2000. In addition to numerous journal articles and book chapters,

he has edited three books: most recently, "Planning, Shortage,

and Transformation" (with A. Simonovits, MIT Press, 2000).

Interviewer Edward Tenner, the author of "Why Things

Bite Back: Technology and the Revenge of Unintended Consequences"

(Vintage Books), is a visiting scholar in the English department at

Princeton University. His essays and reviews have appeared in the

New York Times, the Wall Street Journal, the Wilson Quarterly, U.S.

News & World Report, and Technology Review. He has held visiting

appointments

at the Institute for Advanced Study, Rutgers, and the Woodrow Wilson

Center for Scholars.

Tenner: Let’s start with the origin of the theory of games

and the 1944 treatise theory of games and economic behavior by John

von Neumann and Oskar Morgenstern. Before John Nash arrived on the

scene, what were von Neumann and Morgenstern trying to do with game

theory, and to what extent did their theory achieve it?

<B>Maskin: A game, as formulated by von Neumann and

Morgenstern in their 1944 book, is simply any situation in which each

participant (called a "player") can affect the other players’

payoffs significantly through his or her actions. This is a general

formulation that applies to an enormous variety of circumstances

arising

in social and economic life. In particular, it applies to industries

that consist of only a few big firms. The breakfast cereal industry,

in which Kellogg, Post, and General Mills are the principal players,

is a case in point. In such an industry, a firm must anticipate what

its rivals are going to do in order to figure out what it should do

itself. But to make this forecast, the firm must take account of the

effect its own actions will have on its rivals, since their behavior

will depend on this impact.

Tenner: Was this something that economists had written

about extensively before or was this a new realization of von

Neumann’s

and Morgenstern’s?

Maskin: It was well appreciated that in industries with

small numbers of firms, firms would have to take account of their

impact on one another. There was, in fact, literature in the 19th

century about this, including work by the French economists Cournot

and Bertrand. So the idea of strategic interaction was not original

to von Neumann and Morgenstern. But they provided a general

methodology

for studying such situations. Previous work was limited to particular

examples.

A major result reported in the 1944 book was the "Minimax

Theorem,"

discovered by von Neumann in 1928. Von Neumann was looking at games

in which there are only two players and in which one player’s gain

is equal to the other’s loss (the formal term for this gain/loss

property

is "zero-sum"). He showed that, in such games, each player

has a strategy — a mode of behavior she can follow — that

will guarantee her a reasonable payoff regardless of how the

other player behaves. Such a strategy is called "minimax."

Minimax strategies are so good that they constitute a plausible

prediction

of how experienced or smart players will behave in a two-player

zero-sum

game.

The major drawback of the Minimax Theorem is that many, if not most,

situations of interest in human affairs either involve more than two

players or violate the zero-sum property (or both). For example, the

cereal industry consists of three players and is not zero-sum —

e.g., the players could form a cartel (which would increase all their

payoffs) or conduct a price war (which would harm them all).

What Nash did was to propose a way of predicting what will happen

in games to which the Minimax Theorem does not apply. As it turns

out, his prediction concept (now called "Nash equilibrium")

amounts to the concept Cournot himself proposed over 100 years earlier

for the particular industrial game Cournot was examining. However,

the great advantage of the Nash equilibrium is that it is completely

general. It is applicable to ANY game.

To understand Nash’s concept, let’s consider a two-player game. In

such a game, a Nash equilibrium consists of a pair of strategies,

one for each player, with the property that neither player has the

incentive to deviate from his strategy unilaterally and play another

strategy (i.e. neither player would get a higher payoff from doing

something else, given that the other player sticks with his Nash

equilibrium

strategy). For example, we can think of driving on the highway as

a game in which each driver decides whether to drive on the right

or the left. Notice that everybody driving on the right constitutes

a Nash equilibrium; a unilateral deviation by any single driver could

lead to disaster.

Tenner: A lot of people reading the "Essential John

Nash" will be surprised at the range of brilliant ideas he had

and also at the brevity of his thesis. For something so momentous,

including the bibliography, it is 27 pages. That says something about

the leverage that a profound mathematical idea can have in the real

world. Is that fair to say?

Maskin: One thing that is true about mathematics in

general

is that you can say the same thing mathematically in 27 pages that

it would take 270 pages to say in ordinary English. Mathematics

confers

an economy of expression. Furthermore, the best ideas in mathematical

economics are usually quite simple, and don’t require pages and pages

for their exposition.

The concept of Nash equilibrium has been immensely fruitful. It

remains

far and away the most common method for making predictions in games

that arise in economics.

Tenner: I see from the book that he was a player of games.

Do you think his experience as a poker player contributed to his

insights?

Maskin: Put it this way. I don’t see much reason why being

a good poker player would make you a good game theorist or vice versa.

Parlor games like poker or chess are actually immensely complicated.

In fact, they are so complicated that, except in highly simplified

versions, they really can’t be analyzed very well using game theoretic

methods. The best chess players, for example, would probably learn

little by studying game theory. They practice an art rather than a

science.

Tenner: There is that element of knowing something that

you don’t consciously know, common to most professions. To take a

different tack, do you think the rise of mainframes and PCs was

necessary

to exploit the Nash equilibrium in widely practical applications or

were there already many things that could be done with slide rules

and early mainframes.

Maskin: With some exceptions such as auctions, Nash

equilibrium

has been a tool more for theoretical work, that is, for making

theoretical

predictions (whether in economics, political science, or biology)

than for highly practical applications. And economic theorists don’t

make much use of computers even now. As a theorist, my principal use

of the computer is for word processing.

Tenner: I wasn’t aware of that.

Maskin: Many economists use computers for analyzing large

volumes of data, for number crunching. But those activities aren’t

theoretical.

Tenner: Let’s turn to the applied side. I know that John

Nash worked at the Rand Corp, which took an interest in his thesis.

According to the "Essential John Nash," his model was felt

to be a more realistic representation of the realities of the nuclear

balance of terror than von Neumann’s.

Maskin: This question goes back to the

zero-sum/non-zero-sum

distinction. During the Cold War, it was simply not the case that

a gain for us would necessarily constitute a loss for the Soviets;

there were instances where both sides could gain, for instance,

by signing a treaty.

Wars — whether cold or hot — are not typically zero-sum games,

and so the methods that von Neumann developed are not always

applicable

to them. Nash equilibrium applies more often.

Military strategy was really the first major application of game

theory.

Ironically, in view of von Neumann and Morgenstern’s book title, game

theory did not become a big part of economics until the ’70s, a

surprisingly

long lag. The authors had hoped their subject would take economics

by storm. It did, finally, but only after 30 years.

Tenner: Any single personality who began this?

Maskin: I think that game theory caught on in the ’70s

because economists at that point got interested in certain topics

for which game theory provided ready tools for analysis. For example,

economists became fascinated with interactions that unfold over time,

i.e., with "dynamic" interactions. Before then, economists

had often studied situations to which game theory was in principle

applicable, but these were usually so simple that you didn’t have

to bother learning the formal theory to analyze them. Dynamic

interactions

proved to be sufficiently complex that game theory came in very handy.

Another kind of situation that economists got interested in was one

in which incomplete information is important, i.e., where Player 1

doesn’t know pertinent information that Player 2 has, and vice versa.

To give an example, suppose that a Van Gogh painting is being sold

at auction and two potential buyers are bidding against each other.

The rules of the auction specify that each buyer will submit a sealed

bid, and the winner will be the high bidder. Presumably neither buyer

knows how much the other buyer is willing to bid. Each buyer has to

make a prediction about the likelihood that the other is willing to

bid $3 million or $5 million or whatever. This is very much a game

of incomplete information.

Once again, game theory had developed tools which allowed people

interested

in auctions — and there were lots of such people by the late ’70s

— to make predictions about what would happen.

Thus, with dynamic games and games of incomplete information, game

theory finally came into its own. You go from a landscape in the early

to mid ’70s, where none of the leading economics departments in the

country had game theory courses in their graduate catalogs on a

regular

basis, if at all, to one 15 years later where every

self-respecting

department made game theory a central part of the curriculum. I think

von Neumann and Morgenstern, and for that matter Nash, were too much

ahead of their time to have an immediate effect.

Tenner: Let’s jump ahead to another 25 years or so and 2000.

Last year I attended the lecture of Ken Binmore, the economist from

University College, London, who is a visiting scholar at the

Institute.

He was an advisor to the British government for the $34 billion

auction

of third generation mobile phone lines. It may have been the most

spectacular auction ever.

Maskin: You described it very well. It involved huge sums

of money. All the parties involved — the government running the

auction and the participants bidding in it — paid a great deal

of attention to game theory because it was so important to get things

right.

Tenner: Is it possible to describe for a lay audience

how Nash’s theory helped construct the auction and why so many rounds

were needed to get the highest bid from among 13 bidders?

Maskin: There are basically two main types of auctions:

Sealed-bid auctions, where each buyer makes a bid by writing it on

a piece of paper and sealing it in an envelope; and open auctions,

where successively higher bids are called out openly, until no one

wants to raise the bid any further. The British auction was of the

second type. The reason why there were so many rounds is that bidding

started out low, and it took time for the bids to work their way up

to the stratosphere. The concept of Nash equilibrium was a crucial

tool in enabling the government to predict how companies would bid

in this auction. It was also crucial to individual companies for

predicting

how their competitors would behave.

Tenner: I’m not sure if it bears on Nash equilibrium,

but, experimentally, has it been shown one way or another that the

open auction achieves higher prices for the seller consistently than

the sealed auction?

Maskin: There is no general conclusion about that. Both

theory and experiment suggest it depends on the circumstances.

Tenner: Are there ways for ordinary small and medium sized

companies to use game theory in their daily operations?

Maskin: I think anybody getting an MBA these days is going

to be exposed to a fair amount of game theory. It is now part of the

standard MBA curriculum. Even if an MBA-trained manager doesn’t sit

down and formally analyze a strategic situation as a game, he or she

is likely to invoke game-theoretic considerations informally in making

strategic decisions. Game theory is used all the time in practice

on an informal level. And when stakes are high enough, as they were

in the spectrum auctions, there is a fair amount of formal analysis

as well.

Tenner: Are there particular situations, for instance

in real estate, where consultants will formally apply these methods

in analyzing situations or consulting at auctions?

Maskin: There is quite a booming business in auction

consultation

these days. Consultants give advice both on how to design auctions

and how to bid in them.

Tenner: Turning back to strategic beginnings of modern

game theory, can game theory be applied to issues like nuclear

proliferation

and terrorism in ways that are similar or different from those that

the Rand Corporation was using in the 1950s?

Maskin: There have been major advances in the formal side

of game theory since the ’50s, e.g., the development of tools to deal

with dynamic games and games of incomplete information. So I think

game theorists are better equipped today to analyze issues such as

nuclear proliferation and terrorism than they were in the ’50s.

Tenner: I appreciate your time and your great

understanding

of the history and the present status of game theory.


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