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 payoff-maximizing 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. Non-Bayesian 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 real-world 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 real-life 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 well-developed 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 game-theory 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 cross-fertilization 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 87-991013-4-3
(paperback)
248 pages / $26 / £16

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