
EHUD KALAI
James J. O’Connor Distinguished Professor of
Decision and Game Sciences at the Kellogg School of
Management and Professor of Mathematics at the
College of Arts and Sciences
Northwestern University, USA 
Excerpt from Ehud Kalai's
interview: Question 3. What is the proper role of game
theory in relation to other disciplines?
In my roles
of past president of the Game Theory Society and an editor
of a game theory journal, I recently constructed a list of
areas of activities in game theory and its applications. The
list should give the reader an appreciation of the
interactive nature of game theory.
1. Non cooperative game
theory studies the behavior of
payoffmaximizing players who take into consideration all
strategic and informational parameters.
2. Cooperative game theory studies how considerations
of efficiency, fairness and stability guide the allocations
of profits and costs to coalitions of rational players.
3. Behavioral game theory studies how real players
play games: experimental games played in the lab, and
empirical games played in the real world.
4. Evolutionary game theory studies play guided by
imitation, survival of the fittest, etc.
5. Algorithmic and artificial game theory study
issues of computational, informational, and behavioral
complexity in games played by live players or by computing
machines.
6. Interactive epistemology studies the subject of
knowledge, including knowledge about knowledge.
7. Combinatorial games deal with mathematical
issues unique to games.
8. NonBayesian decision theory concentrates on
decision making under uncertainty, when relaxing or
replacing the Bayesian assumptions made in the classical
theory.
9. Neurological studies of games deal with
physiological activities observed during the play of a game.
10. Economic games use the above tools to gain
insights into strategic economic interaction and the
performance of economic systems.
11. Political games use the above tools to gain
insights into strategic political behavior and the
performance of political and social systems.
Game theory
has been described by some as the physics of the social
sciences. I think that another useful analogy involves
probability and statistics. Probability theory offers a
language and rules for dealing with uncertainty, and
statistics offers tools for realworld applications. These
theories are designed to deal with uncertainty, no matter
where it arises. Similarly, game theory offers a language
and rules to deal with strategic interaction, wherever it
arises. The Arthur Andersen and Baxter applications
described earlier suggest an interesting parallel with
statistics. When dealing with a reallife application, a
statistician must choose the best among an available set of
models: a classical approach, a nonparametric approach, a
Bayesian approach, etc. An applied game theorist must
choose between a coalitional model, a strategic model, or a
hybrid of several models.
But thinking
of game theory as similar to probability and statistics
makes the relationship to other sciences clear. First, like
probability theory, a welldeveloped game theory is
foundational in any subject that deals with interaction.
Second, in practical applications that involve strategic
interaction, there is no way to avoid using game theory.
However, following the practice of statistics, it may be
necessary to have several different gametheory models, with
the user choosing the appropriate model for the application.
As we have
discussed, the interaction of game theory with economics
over the previous century has concentrated mostly on
theoretical applications. And indeed, in a similar manner
to the use of probability theory, the use of game theory has
become unavoidable in essentially all rigorous studies of
strategic economic phenomena. We see that political science
is going through a similar progression, even at a more
fundamental level. Unlike economics, were much formal
modeling was done prior to the arrival of game theory
(through equilibrium models of supply and demand, for
example), the initial formal modeling of political systems
had to start with the use of game theory.
The
interaction with evolutionary biology and computer science
is interesting because there is a reciprocal fertilization
between game theory and these other subjects. Since
evolutionary biology studies interaction among species, it
is natural to apply game theory there. But the reverse is
also true. Evolution theories describe how the behavior of
species evolves, without resorting to rationality but using
concepts such as imitation, survival of the fittest, etc.
An important finding there is that despite no reliance on
rationality, species’ behavior converges to what is
predicted by Nash equilibrium. This is an important
connection. It makes both theories more robust, and it is
the subject of much current research.
Similar
reciprocal fertilization is present in the interaction of
game theory and computer science. Both game theory and
computer science share a common goal: the mathematization of
rational choices and behavior. Historically, however,
computer science concentrated mostly on algorithms that
generate rational choices, subject to complexity
constraints. For a long time it ignored strategic and
interactive aspects in systems that involved more than a
single decision maker. Game theory, on the other hand,
ignored issues of computation and complexity and
concentrated mostly on the strategic interactive aspects.
In recent years, we have seen a growing interaction and
crossfertilization between the two fields.
Read
the remaining part of Ehud Kalai's interview in Game Theory: 5
Questions, edited by Vincent F. Hendricks and Pelle
Guldborg Hansen. The book is released in April 2007 by
Automatic Press / VIP.
ISBN
8799101343
(paperback)
248 pages / $26 / £16
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