On Kalai (1995)

Yoav Shoham Computer Science Department Stanford University August 22, 2007

One of the exciting developments in both computer science and in the past decade is the dramatic increase in the interaction between the two fields. This is due in no small measure to Ehud Kalai’s tireless efforts to pro- mote these interactions, both in his writings and his substantial organizational roles (in particular, in his editorship of Games and Economic Behavior, and his leadership role in the International and its quad-annual conference). This has not been a new calling for Ehud. Already in [1] he reviewed a number of areas of interaction between these two fields (as well as ). In this short note I look back at his selection of topics, and ask to what extent they reflect the current research foci. As we will shall see, Kalai’s 12-year-old summary is surprisingly current, and where it diverges from current foci, it exposes important areas for further research. In [1] Ehud discusses the following topics:

1. Graphs in games 2. Multi-person operations research 3. The complexity of playing a game 4. The complexity of solving a game 5. Modeling bounded rationality

When one looks at the body of research that takes place today at the inter- section of computer science and game theory, one can roughly identify five foci of interest:

a. Compact and otherwise specialized game representations (for example, graphical games) b. Algorithmic mechanism design and auctions c. Complexity of, and algorithms for, computing solution concepts

1 d. Multi-agent learning

The mapping between these two lists is 1–a, 2–b, 3–, 4–c, 5–, –d. Some observations:

• The degree of the matching is striking. • The high-level matching obscures specializations that have emerged in the past 12 years. For example, specific game structures studied are inspired by internet phenomena such as reputation or social networks. Similarly, some specific auction types have attracted particular attention, such as combinatorial auctions and keyword auctions. • The biggest piece missed by Kalai is multiagent learning, somewhat ironic in light of the fact that one of the seminal publications in the area is [3]. • On the other hand, Kalai points to several areas that have not yet been picked up substantially by the community in recent years, in particular, the closely related items 3 and 5 on his list.

In my view, some of the most difficult and most exciting areas to tackle are these under-explored areas. In his presidential address in the Games 2004 Congress [2], Kalai reprised the three stages of any science as discussed by von Neumann and Morgenstern, culminating with the stage that includes genuine applications of the underlying theory. Elegantly backing off from the assump- tions of perfect rationality and reasoning capability may be key to achieving this third stage.

References

[1] Ehud Kalai. Games, computers, and O.R. In ACM/SIAM Symposium on Discrete Algorithms, 1995. [2] Ehud Kalai. Presidential address, the second world congress of the game theory society. Games and Economic Behavior, 2007. Special issue, to appear (P. Reny, ed.). [3] Ehud Kalai and Ehud Lehrer. Rational learning leads to . Econometrica, 61(5):1019–1045, 1993.

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