An interview with robert aumann
Yüklə 2,96 Mb. Pdf görüntüsü
|
INTERVIEW WITH ROBERT AUMANN 717 A: It’s a way of talking about many sciences, many disparate disciplines. Unlike other approaches to disciplines like economics or political science, game theory does not use different, ad-hoc constructs to deal with various specific issues, such as perfect competition, monopoly, oligopoly, international trade, taxation, voting, deterrence, animal behavior, and so on. Rather, it develops methodologies that apply in principle to all interactive situations, then sees where these methodologies lead in each specific application. But rather than being an umbrella for all those disciplines, it’s perhaps better to think of it as a way of thinking about a certain aspect of each—the interactively rational aspect. There are many things in these disciplines that have nothing to do with this aspect. In law, in computer science, in mathematics, in economics, in politics, there are many things that have nothing to do with game theory. It is not like a unified field theory, which would cover all of gravitation, magnetism, and electricity. H: Perhaps it is like mathematics applied to other sciences, which is a tool, a language for formalizing and analyzing. A: That’s an interesting analogy. Mathematics helps in certain aspects of many sciences—those given to formalization. Game theory is similar in that respect: it helps in many disciplines, specifically in their interactively rational parts. Figure 6 is a stylized representation. H: The Game Theory Society was established in ’99. You were the first, found- ing president, up to 2003. By now you should have a good overview of what game theory is, and of what the Game Theory Society is.
time to have a tool for gathering game theorists in all kinds of senses. Conferences, journals, the Web. When discussing my education, I mentioned that at City College there were a couple of tables reserved for the more dedicated math students. People would come between classes, sit down, have an ice cream soda, and talk about math. The Game Theory Society is the game theory table in the cafeteria that’s called the world. It is a place where people can discuss game theory and exchange ideas, in various senses and various ways. H: Do you have any thoughts on where game theory is going? A: It is difficult to tell. It is very hard to know where things are going. In the presidential address at the Game Theory Society Congress in Bilbao in 2000 [81], 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 find 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. H: Do you expect a Tower of Babel syndrome to develop? A: 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. 718 SERGIU HART F IGURE 6. The blooming of game theory. H: What is definitely 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 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 benefits from everybody else. Take physics or mathematics. I wouldn’t understand what algebraic topology does nowadays. Somebody in combinatorics may understand something about probability, but wouldn’t understand some of the things we do in game theory. Nevertheless, mathematics is a single discipline. Would you like to say anything about the different approaches in game theory? For example, mathematical vs. conceptual; axiomatic and cooperative vs. strategic and noncooperative. Why is it that there are so many approaches? Are they con- tradictory or are they just different? And how about people who think that some approaches in game theory are valid, and other approaches are not?
tive, strategic games, who think that cooperative (coalitional) game theory is less important, not relevant, not applicable.
INTERVIEW WITH ROBERT AUMANN 719 Let me backtrack and describe what we mean by noncooperative or strategic game theory, vis-`a-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, 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 equilibrium con- cepts and is based on a precise description of the game in question. 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 the- ory is better suited to situations like coalition formation or the formation of a government in a parliamentary democracy or even the formation of coalitions in international relations; or, what happens in a market, where it is not clear who makes offers to whom and how transactions are consummated. Negotia- tions in general, bargaining, these are more suited for the coalitional, cooperative theory.
H: 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.
these approaches are not disparate. In order to make a bridge like that you have to define 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 defined. The big advantage of the cooperative theory is that it does not need a precisely defined 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 defines 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 significant group of people in strategic game theory who have an attitude towards coalitional game theory similar to that of pure mathematicians towards applied mathematics fifty years ago. They looked down their noses and
Yüklə 2,96 Mb. Dostları ilə paylaş:
|