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发帖数: 197 | 1 http://www.princeton.edu/~dixitak/home/nashenco.pdf
John Nash % Founder of Modern Game Theory
by Avinash Dixit
Princeton University
If economists are ranked according to the value of their contribution per
paper they wrote,
then John Nash will have an excellent claim for the top spot, with the
possible exception of
Frank Ramsey. In a short but brilliant career, he wrote just half a dozen
papers that liberated
noncooperative game theory from the two-person and zero-sum confines of von
Neumann and
Morgenstern, greatly improved upon their solution for an important class of
cooperative games,
and laid the foundations of the approach that has come to dominate thinking
and modeling in
economics, politics, business studies, and other disciplines as well.
John Nash burst upon the economics scene in 1950 with two papers that have
defined the
subsequent direction of economic applications of game theory in both its
cooperative and
noncooperative modes. The latter line was launched by his simple and elegant
general proof of
the existence of a noncooperative equilibrium in n-person games. In Nash’s
framework each
player takes the others’ strategies as given and chooses his own strategy;
equilibrium is where all
these choices are mutually consistent. In the standard Marshallian or
Walrasian theory of
competitive markets, each individual consumer or firm takes the market
prices as given and
makes or her own purchase and sale decisions; the equilibrium price is where
all these choices
are mutually consistent. Therefore Nash’s approach is a natural extension
to strategic situations
of the familiar economic framework of choice and equilibrium. What is more,
Nash’s theorem
works for any number of players, and with arbitrary mixtures of common
interests and conflicts
of interest; this is needed in economics where many people interact, and
there are potential
mutual gains from trade as well as distributive conflicts. All this makes
Nash equilibrium such an
appropriate way to model interactions of rational individuals that it has
taken over the field of
economics and spread to many other fields. Writers using this theory no
longer feel the need to
cite Nash’s paper explicitly, but merely say "Nash equilibrium". If Nash
got a dollar for every
time someone wrote or said "Nash equilibrium", he would be a rich man.
Some of the best ideas in science are simple, even obvious, once someone has
thought of
them. These are the papers that cause you to smack your forehead and say "
Why didn’t I think of
that?" With Nash’s paper I am spared that personal chagrin because I was
only five years old at
the time, but I am surprised that others including the legendary von Neumann
did not think of it.
In my view it makes Nash’s contribution that much more valuable.
Nash’s contribution to the theory of bargaining was equally pathbreaking.
Before him,
economists thought that the outcome of bilateral bargaining was
indeterminate, dependent on
some vaguely defined "bargaining powers" of the participants about which
economics could say
little. The more formal cooperative game-theoretic approach of von Neumann
and Morgenstern
was equally indeterminate; it offered as the solution the whole set of
Pareto efficient allocations.
Nash took the cooperative approach, and laid down a set of properties such
that there would be a
unique solution satisfying them for each bargaining problem in a large class
of such problems.
The solution had some features of fair arbitration to divide up the players
’ gains from the deal,
but this was not central to Nash’s aim. He thought of the outcome as
resulting from some
unspecified process of negotiation or strategizing by the individual
bargainers each acting in his
own interests; the cooperative solution was intended as a device to cut
through the complex
details of this process and be useful for predictive purposes. The idea of
elaborating this
connection, so that "steps of negotiation become moves in a larger non-
cooperative game", has
become known as the "Nash program". The best known and most influential
contribution to this
line of research is Ariel Rubinstein’s work on the bargaining problem. But
even before that
appeared, many applications in labor economics and international trade had
used Nash’s
axiomatic and cooperative solution with great success for the predictive
purpose he intended.
Laboratory experiments have become an important method of testing theories
of behavior
and interaction, and Nash was a pioneer here too. In the early 1950s at RAND
, in collaboration
with Kalisch, Milnor and Nering, he carried out experiments involving games
of bargaining and
coalition formation. Equally foresighted was his incisive criticism of
others’ experiments on the
prisoners’ dilemma, where a pair of players played the game many times, and
were found to
cooperate a great deal: "The flaw in the experiment as a test of equilibrium
point theory is that
the experiment really amounts to having the players play one large multi-
move game. Onecannot just as well think of the thing as a sequence of
independent games as one can in zero-sum
cases." This could be the first glimpse of the possibility of tacit
collusion in repeated games,
which has become such an important topic in economic and political
applications.
I have limited myself to discussions of Nash’s work in economics, because I
lack the
expertise to discuss his contributions to mathematics % embedding of
Riemanian manifolds,
existence of solutions for parabolic and elliptic partial differential
equations % which many
mathematicians regard as even more important than his Nobel-winning work in
economics, and
which made him a leading candidate for a Fields Medal.
Nash accomplished so much in so few papers that one wonders what would have
happened if his academic career had continued in the normal way after 1960.
Would he have
continued to produce equally startling papers at the same rate? Alas, we
will never know. _< @\
J,@4 N48@LF4 "B@2<,F6,4 <,@H. (He whom the gods love dies young.) That is
what happened
to Frank Ramsey. In John Nash’s case, gods must have loved his mind so much
that they took it
away from us for almost thirty years. But gods are not heartless; they must
have heard the
prayers of John’s many dedicated friends and even more numerous admirers,
and have at last
restored his mind to us. He is actively engaged in research that continues
the Nash program he
laid down almost half a century ago, and is developing an approach to many-
player bargaining
that replaces the cooperative coalitional formation by a noncooperative
process of election of
designated negotiating agents. We await the results eagerly. |
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