in Bilbao in 2000 [Aumann (2003a)], I discussed some directions for

research in the future.

Let me say something of a more general nature. People are pushing in

different directions; we are going to ¬nd a spreading of the discipline

among different people. Some people go in a very strongly mathematical

direction, very deep mathematics. We will see a separation of the more

mathematical branches from the more applied branches like economic

applications. We™ll see a lot of experimental and engineering application

of game theory. People in game theory will understand each other less in

the future.

Hart: Do you expect a Tower of Babel syndrome to develop?

Aumann: It is not something that I would like, but it™s a sign of

maturity. Tower of Babel syndrome is a very good way of putting it.

Hart: What is de¬nitely true is that from a small community where

essentially everybody could understand everybody else, game theory

has grown to a big “city,” where people are much more specialized. As in

any developing discipline, it™s natural that everybody goes deeper into one

An Interview with Robert Aumann 367

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Figure 15.6

of the aspects and understands less and less of the others. Nevertheless, at

this point there is still interplay between the various aspects and approaches,

so everybody bene¬ts from everybody else. Take physics or mathematics.

I wouldn™t understand what algebraic topology does nowadays. Some-

body in combinatorics may understand something about probability, but

wouldn™t understand some of the things we do in game theory. Never-

theless, mathematics is a single discipline.

Would you like to say anything about the different approaches in game

theory? For example, mathematical versus conceptual; axiomatic and co-

operative versus strategic and noncooperative. Why is it that there are so

many approaches? Are they contradictory or are they just different? And

how about people who think that some approaches in game theory are

valid, and other approaches are not?

Aumann: You are quite right that there is a group of people, working

in noncooperative, strategic games, who think that cooperative (coali-

tional) game theory is less important, not relevant, not applicable.

Let me backtrack and describe what we mean by noncooperative or

strategic game theory, vis-à-vis cooperative or coalitional game theory.

Strategic game theory is concerned with strategic equilibrium”individual

utility maximization given the actions of other people, Nash equilibrium

and its variants, correlated equilibrium, that kind of thing. It asks how

people should act, or do act. Coalitional game theory, on the other hand,

368 Sergiu Hart

concentrates on division of the payoff, and not so much on what people

do in order to achieve those payoffs.

Practically speaking, strategic game theory deals with various equilib-

rium concepts and is based on a precise description of the game in ques-

tion. Coalitional game theory deals with concepts like the core, Shapley

value, von Neumann“Morgenstern solution, bargaining set, nucleolus.

Strategic game theory is best suited to contexts and applications where

the rules of the game are precisely described, like elections, auctions,

Internet transactions. Coalitional game theory is better suited to situ-

ations like coalition formation or the formation of a government in a

parliamentary democracy or even the formation of coalitions in inter-

national relations; or, what happens in a market, where it is not clear who

makes offers to whom and how transactions are consummated. Negoti-

ations in general, bargaining, these are more suited for the coalitional,

cooperative theory.

Hart: On the one hand, negotiations can be analyzed from a strategic

viewpoint, if one knows exactly how they are conducted. On the other

hand, they can be analyzed from a viewpoint of where they lead, which

will be a cooperative solution. There is the “Nash program””basing

cooperative solutions on noncooperative implementations. For example,

the alternating offers bargaining, which is a very natural strategic setup,

and leads very neatly to the axiomatic solution of Nash”as shown by

Rubinstein and Binmore.

Aumann: These “bridges” between the strategic and the coalitional

theory show that these approaches are not disparate. In order to make a

bridge like that you have to de¬ne precisely the noncooperative situation

with which you are dealing. One of the bridges that we discussed earlier

in this interview is the Folk Theorem for repeated games. There, the

noncooperative setup is the repeated game. When you have a bridge like

that to the noncooperative theory, the strategic side must be precisely

de¬ned. The big advantage of the cooperative theory is that it does not

need a precisely de¬ned structure for the actual game. It is enough to say

what each coalition can achieve; you need not say how. For example, in a

market context you say that each coalition can exchange among its own

members whatever it wants. You don™t have to say how they make their

offers or counteroffers. In a political context, it is enough to say that any

majority of parliament can form a government. You don™t have to say

how they negotiate in order to form a government. That already de¬nes

the game, and then one can apply the ideas of the coalitional theory to

make some kind of analysis, some kind of prediction.

You asked about the sociology of game theorists, rather than game

theory. There is a signi¬cant group of people in strategic game theory

An Interview with Robert Aumann 369

who have an attitude towards coalitional game theory similar to that of

pure mathematicians towards applied mathematics 50 years ago. They

looked down their noses and said, “This is not really very interesting;

we™re not going to sully our hands with this stuff.”

There is no justi¬cation for this in the game-theoretic sociology, just as

there was no justi¬cation for it in the mathematics sociology. Each one

of these branches of the discipline makes its contribution. In many ways,

the coalitional theory has done better than the strategic theory in giving

insight into economic and other environments. A prime example of this

is the equivalence theorem, which gave a game-theoretic foundation for

the law of supply and demand. There has been nothing of that general-

ity or power in strategic game theory. Strategic game theory has made

important contributions to the analysis of auctions, but it has not given