Amsterdam, December 6, 2004

The ninth edition of the workshop on Games in Logic, Language and Computation (GLLC9) will be held on Monday December 6, 2004.

The informal workshop series "Games in Logic, Language and Computation" focuses on applications of game theory in linguistics, logic, and computer science, as well as on the (logical) foundations of game theory. Earlier meetings have taken place in Amsterdam, Groningen, Nunspeet, and Utrecht.

Sponsors of the workshop are the Institute for Logic, Language and Computation, and the Beth Stichting.

The workshop is open to all interested. There is no entrance fee.

For more information, please contact debruin@science.uva.nl.

University of Amsterdam, Building A, Roetersstraat 15, room A-102. For directions please click here.

Abstracts below.

Wlodek Rabinowicz, Pragmatic arguments for rationality constraints

An argument of this kind purports to show that a violator of a constraint can be exposed to a decision problem in which he will act to his guaranteed disadvantage. Dramatically put, he can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic Dutch Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. These arguments share a common feature. If the violator of a constraint is logically and mathematically competent, he can be exploited only if he is disunified in his decision-making; i.e., if he decides various issues separately, rather than jointly. In my talk, I will explore some of the consequences of this observation.

Paul Harrenstein, Solution concepts as indicators

Game theory provides a framework for the formal analysis of social interaction. In their "The Theory of Games and Economic Behavior" von Neumann and Morgenstern propounded the view of social interaction presenting a problem that warrants the development of an entirely new mathematics. In particular, game theoretical solution concepts should take over the role of the notion of optimality in order to obtain a proper grasp of the subject matter at hand. Since then, a myriad of solution concepts has been proposed. But what exactly are these solution concepts and what are they supposed to do for the theoretician or scientist in the field? In this talk I wish to defend Aumann's position concerning this issue, which is that game theoretic solution concepts ar to be taken as indicators. They are meant to single out the strategically conspicuous features of a game situation and helps us reason about them and to attain a proper grasp of social interaction. On this view, the important question would seem concern which conclusions to draw from a particular course of action complying with a solution concept in a game situation, rather than the development of a solution concept that is either discriptively fully adequate, normatively feasible or otherwise a game theoretic panacea. To rephrase the issue in a rather more Wittgensteinean fashion, what are a solution concepts conditions of use? This philosophical outlook is illustrated by considering the Nash equilibrium solution concept and the allegedly unfortunate solutions it provides in the case of the Prisoner's Dilemma and the Centipede game. We will defend Nash equilibrium on the basis that the very Pareto inefficiency of the solutions in these cases points at a significant feature of the games at hand. A consequence of the view of game theoretic solution concepts as indicators seems to be that they should also facilitate the mutual comparison of the strategic features of different game situations. If time permits, we will argue that Nash equilibrium does rather less well in this respect.

Marc Pauly, Debating the discursive dilemma

The discursive dilemma raises the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. Various impossibility theorems have shown the difficulty of this task. In this talk, I will discuss different ways to arrive at possibility results.

Merlijn Sevenster, Using weak dominance as a semantics for IF-logic

Game theoretical stances have been proposed in many area's (viz. linguistics, computer science and mathematics) to shed a more intuitive light. In this tradition, game theory has also been used to provide a semantics for Hintikka's independence friendly logic (IF-logic). IF-logic abstracts from the Fregean assumption that quantifiers' scope and binding coincide. Its ''game theoretical semantics'' typically consider the checking of an IF-formula as a evaluation game with imperfect information. However, it has been argued (viz. van Benthem) that the players in such evaluation games do not suffer from the kind of imperfect information that one finds in game theory. In my talk, I will present several semantics for IF-logic, that are more game theoretically involved. That is, they are based on the game theoretical notion of dominance. I will address some examples of the presented semantics and discuss their plausibility.

Johan van Benthem, Logic on the move

As a game proceeds, players receive new information which affects their knowledge, while also leading them to revise beliefs about both their past and future. This requires a move-by-move analysis of information flow. In this talk, I use a temporal-epistemic-doxastic logic and its branching-time models to clarify a number of issues: (a) where/how to encode relevant hypotheses that agents can entertain about the course of a game, (b) how to describe different logical types of agent on top of a base logic that works for the setting as such, (c) how to mimick 'global update' of beliefs about the future via 'local update' in dynamic-epistemic logics.

Ref. J. van Benthem, June 2004, Update and Revision in Games', class note, department of philosophy, Stanford.

Olivier Roy and Sieuwert van Otterloo, Preference Logic and backward induction

Game theoretical solution concepts, such as backward induction, are grounded in the preferences of the players. Thus, reasoning about how intelligent agents will behave in a game situation involves reasoning about their preferences. In this talk we will first introduce a complete logic to reason about preferences. Then we show how to embed it in a more expressive logic that can talk about games in extensive form and their par excellence solution concept : backward induction.