The spirit of Kellogg: research and teaching
Professor Ehud Kalai
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
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
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
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.