Web Exclusive

The spirit of Kellogg: research and teaching

Professor Ehud Kalai

Professor Ehud Kalai

Ehud Kalai, the James J. O'Connor Distinguished Professor of Decision & Game Sciences, and Director of the Center for Strategic Decision-Making, is a thought-leader in the realm of game theory. He shared his ideas with Kellogg World about what makes Kellogg such a dynamic research environment.

What is it that proves most compelling for you as both a teacher and researcher working at the Kellogg School?

I enjoy teaching Kellogg's students at all levels, MBA, Executive Education and in the PhD program. Bringing to the classroom the findings of theoretical research, and putting this material in front of bright business students of all levels, is highly beneficial to the development of both research and teaching. The teaching of subjects such as strategy or operations management at most business school was completely revolutionized over the last 20 years - due to research and classroom implementation done at Kellogg. For example, when I join Kellogg as a young game theorist in 1975, neither the students nor the faculty knew the concept of Nash equilibrium, a concept at the very frontier of Game Theoretic research at that time. Today, it is part of the common jargon in a business school curriculum, known and used in many of our courses. But also the converse is true. Work that I have done with executive students from Baxter Corporation, for example, leads me to a research agenda that I did not think important a few years ago.

How would you characterize the research climate here?

The research atmosphere at Kellogg is awesome! You could spend all your working hours attending first-rate research seminars in your area, without having time left to do other work. We constantly get requests from researchers who want to move here, or at least come and visit for a short time. Being here exposes one to knowledge and a learning atmosphere at a caliber rarely observed in other places. Not only do we have the leading researchers in many areas, but we also have an unusually large number of such people. When you put together the researchers from the various Kellogg departments and from other departments at NU, as is the case in many of our seminars, there is an overwhelming breadth and depth of knowledge.

What elements are responsible for creating this dynamic teaching and research community at the school?

Several factors contribute to the productive research atmosphere at Kellogg. We bring in people who are strong in fundamental areas, such as economics, mathematics, and operations research, and let them interact with each other, with the students and with the business community. Exposing creative, able people to interdisciplinary ideas and to business applications turns out to be very productive. For example, I came here for a one-year visit from my home university where I had a position in the mathematics department. I was somewhat reluctant to come, thinking that for my subject I was better off being in a mathematics department than in a business school. At the end of the year there was no question in my mind. The back-and-forth interaction between the local economists and me was extremely interesting, intellectually satisfying, and led to great contributions to both sides.

We now see similar interdisciplinary interaction between game theorist, operations people and political scientists. Again, Kellogg is leading the way in the developments of these fields.

Are there other dynamics at work that make Kellogg a powerful place for research?

A very important characteristic of Kellogg is our ability to adapt fast, recognize important research directions and take advantage of opportunities. This is due to the tremendous resources we have, but also to the particular structure of the school, which allows for quick decision-making. Unlike other places, where decisions require complicated approval procedures by many committees, we can make overnight decisions and have them approved by the deans within hours. One of the selling points of Kellogg to me was the way I was hired. I was interviewed, in Tel Aviv, by a senior Kellogg faculty member, and the next day I had a written job offer in my hands (sent by a telegram, since there was no e-mail then). This was a very impressive message about the efficiency of the organization.

What are some aspects of your research that prove most interesting to you at present?

Over the last two dozen years, the Nash equilibrium paradigm took over much of the quantitative analysis in economics and management. But it was not clear whether, and how, players converge and learn to play such equilibrium. Over a period of 10 years, with the collaboration of other faculty members from the MEDS department, we developed the models that show why, and in what circumstances, statistical learning of opponents' behavior would lead in the long run to a Nash equilibrium play. Now I am investigating the question of how an equilibrium play reacts to changes in the number of players. In particular, what are the special properties of equilibria in games with many anonymous players?

Have you encountered any surprising developments along the way?

Somewhat surprisingly, we have discovered that games may become easier to play and to predict as the number players becomes large. This is surprising because as the number of players increases, there are more parameters of uncertainty (for example, the unknown behavior of a greater number of opponents) that a players faces. On the other hand, when the number of players is very large, laws of large numbers may take effect, and the aggregate behavior becomes predictable. So the feeling now is that very small and very large games are easy to deal with, but moderate size games may be the most difficult to analyze.

Another surprising finding is that when the number of players is large, Nash equilibria become highly robust. They are immune to information leakage, changes in the order of play and revision possibilities. So the predictions made by Nash equilibrium in large games are more reliable.

We also learned a surprising relationship between making optimal decisions using randomization, and solving for optimal decision rules that are simple. It was well established that in single-person decision making, optimal behavior does not require randomization. If, however, we desire to find an optimal simple rule, then the above rule is no longer true. There are stochastic simple rules that outperform all deterministic ones. This observation gives rise to many new questions that we now study.

In what broader context would these research findings have the most potential impact?

Many economic and political games involve a large number of participants. Also much of the strategic interaction on the Internet involves a large number of such players. So being able to better predict the behavior of people in such interactions may lead to a large number of applications.

One nice illustration is the evolution of standards. Would individual buyers choose a computer of type I or type II? Assume that each consumer has a preference for one type or the other, but also that he can benefit from matching a large number of other buyers. It is easy to see that in such situations two types of outcomes are strategically stable: all consumers buy type I or all buy type II. But it turns out that if the number of buyers is large, a mixed outcome, with a fraction of the buyers choosing type I and the remaining choosing type II is also strategically stable.

What developments in your field of inquiry could be on the horizon -- perhaps developments we can now only begin to glimpse? How might these developments impact the corporate and political worlds?

A major question for game theory is to predict the behavior of players that are less than fully rational, and to recommend optimal policy to players dealing with less than fully rational opponents. We also need to learn to deal with situations where the rules of the game are not fully known to the players or the analysts. We are beginning to see small progress in these directions, but we are very far from really solving the problems.

These are very important questions because essentially every business, every organization and every individual repeatedly have to make choices in such complicated unspecified environments. So being able to answer such questions will dramatically increase the applicability of game theory, and put it at a similar, or higher level, than established old mathematical fields such as statistics.