http://www.dagstuhl.de/11101

### 06. – 11. März 2011, Dagstuhl Seminar 11101

# Reasoning about Interaction: From Game Theory to Logic and Back

## Organisatoren

Jürgen Dix (TU Clausthal, DE)

Wojtek Jamroga (University of Luxembourg, LU)

Dov Samet (Tel Aviv University, IL)

## Auskunft zu diesem Dagstuhl Seminar erteilt

## Dokumente

Dagstuhl Report, Volume 1, Issue 3

Teilnehmerliste

Gemeinsame Dokumente

Dagstuhl's Impact: Dokumente verfügbar

Programm des Dagstuhl Seminars [pdf]

## Summary

The group (48 participants from 13 countries) convened in Dagstuhl in March 2011, for a five day meeting.

Of particular importance was the choice of the participants and the areas they working in, namely: (1) classical game theory, (2) mathematical logic, and (3) economics. While there are some relations between these areas, we felt that more work should be done on the overlapping parts to make tools and methods from one area available in the others (if possible).

In particular, we wanted to find answers to the following questions:

- Are existing models of interaction adequate? Can models used by different disciplines be integrated in a meaningful way?
- How can we use game-theoretical concepts to construct logics that support strategic reasoning? What are the necessary features of such logics?
- How can epistemic-logic reasoning and definitions lead to the definitions of new solution concepts is strategic-form games?
- How can epistemic and strategic logic be adapted to the empirical findings from game theoretic laboratory experiments, manifesting bounded rationality of a variety of types?
- How can issues of computational complexity be addressed vis-a-vis the demand for efficiency/optimality in the design of economic mechanisms under asymmetric information?

The seminar resulted in making the first step towards answering these questions. We did not obtain the ultimate formal answers, especially in the sense of enabling implementation in the form of ready-to-use tools and methodologies. However, researchers with different background shared their views on how games and multi-agent systems can be modeled and reasoned about, which led to several discussions on fundamental questions (like: *what features/concepts are indispensable when analyzing interaction between agents?*). In particular, the issue of whether probabilities (and, more generally: quantities) are necessary to give good account on how agents interact was hotly debated.

The results of the seminar were somewhat constrained by the unbalanced composition of participants. We had invited equally many researchers from computer science (especially computational logic) and economics (game theory). However, while most computer scientists accepted our invitation, the same did only a few economists. This is probably due to the fact that Dagstuhl seminars have an extremely high reputation within computer science, but they are relatively unknown in other disciplines.

In consequence, the synergy between different views of interaction occurred only partially. In our opinion, it was especially fruitful on the basic level. That is, economists and computer science logicians learned about the basic models and patterns of analysis used in the other discipline. Even more importantly, they exchanged views on what *research questions* are relevant and viable when analyzing game-like interaction.

Most synergy occurred within the subgroup of participants coming from the community of *modal logic in computer science*. Talks on modal logic-related topic triggered intensive discussion and ideas for joint research which are currently being pursued by several participants.

We thank the Dagstuhl staff for a very fruitful and interesting week. We are planning a special issue (in Annals of Math and AI) as a concrete outcome of the seminar. Moreover, it was a general consensus that a follow-up seminar would be highly interesting -- this time with more specific topics being the focus. The follow-up is currently in the planning phase.

## Classification

- Semantics / Formal Methods
- Verification / Logic

## Keywords

- Rationality
- Solution concepts
- Game theory
- Computational economics