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This interview with Eric Maskin by Edward Tenner was prepared for
the January 2, 2002 edition of U.S.
1 Newspaper. All rights reserved.
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
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
The anecdote is hokum, of course, and much of the movie embellishes,
even fictionalizes, the facts. The truth can be found in Nash’s
"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
of Technology, and when he received his Ph.D. from Princeton
he was just 21 years old. He taught at Princeton, New York University,
and Massachusetts Institute of Technology. He worked at several
institutions including the Institute for Advanced Study, Rand
and Courant Institute. Although Nash had national security clearance
for a time, he never really worked in the code-breaking field of
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
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.
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,
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).
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
at the Institute for Advanced Study, Rutgers, and the Woodrow Wilson
Center for Scholars.
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
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.
about extensively before or was this a new realization of von
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
for studying such situations. Previous work was limited to particular
A major result reported in the 1944 book was the "Minimax
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
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
of how experienced or smart players will behave in a two-player
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
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.
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?
is that you can say the same thing mathematically in 27 pages that
it would take 270 pages to say in ordinary English. Mathematics
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
far and away the most common method for making predictions in games
that arise in economics.
Do you think his experience as a poker player contributed to his
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
you don’t consciously know, common to most professions. To take a
different tack, do you think the rise of mainframes and PCs was
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.
has been a tool more for theoretical work, that is, for making
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.
volumes of data, for number crunching. But those activities aren’t
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.
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
to them. Nash equilibrium applies more often.
Military strategy was really the first major application of game
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
long lag. The authors had hoped their subject would take economics
by storm. It did, finally, but only after 30 years.
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
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
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
basis, if at all, to one 15 years later where every
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
He was an advisor to the British government for the $34 billion
of third generation mobile phone lines. It may have been the most
spectacular auction ever.
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
how Nash’s theory helped construct the auction and why so many rounds
were needed to get the highest bid from among 13 bidders?
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
how their competitors would behave.
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?
theory and experiment suggest it depends on the circumstances.
companies to use game theory in their daily operations?
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
in real estate, where consultants will formally apply these methods
in analyzing situations or consulting at auctions?
these days. Consultants give advice both on how to design auctions
and how to bid in them.
game theory, can game theory be applied to issues like nuclear
and terrorism in ways that are similar or different from those that
the Rand Corporation was using in the 1950s?
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.
of the history and the present status of game theory.
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