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Epistemic Game Theory and Modal Logic
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Epistemic Game Theory and Modal Logic

A special issue of Games (ISSN 2073-4336).

Deadline for manuscript submissions: closed (31 July 2010) | Viewed by 47385

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Herbert Gintis

E-Mail Website
Guest Editor
External Professor, Santa Fe Institute and Professor of Economics, Central European University, 15 Forbes Avenue, Northampton, MA 01060, USA
Interests: game theory; the rational actor model in economic theory; experimental economics; anthropology

Special Issue Information

Dear Colleagues,

The contemporary culture of game theorists and experimentalists was formed in the period 1980-1995, and is virtually free of understanding of the role of the modal logic of knowledge and belief in evaluating models of rational behavior and their equilibrium properties. There is, of course, a specialized literature, including Nobel prize recipient Robert Aumann and his students, but this is ill-understood and indeed widely ignored outside this circle of experts. As a result, most economists simply do no know what the implications of rationality really are.
I want papers in this special issue to show the relevance of epistemic game theory for the working economist and experimentalist. I tried to go some distance towards this goal in my recent book, The Bounds of Reason (Princeton, 2009), but there is much work to be done and much misinformation to be corrected.

Prof. Dr. Herbert Gintis
Guest Editor

Keywords

  • epistemic game theory
  • epistemic logic
  • modal logic

Related Special Issue

Published Papers (5 papers)

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529 KiB  
Article
Toward a Theory of Play: A Logical Perspective on Games and Interaction
by Johan Van Benthem, Eric Pacuit and Olivier Roy
Games 2011, 2(1), 52-86; https://doi.org/10.3390/g2010052 - 16 Feb 2011
Cited by 38 | Viewed by 14824
Abstract
Logic and game theory have had a few decades of contacts by now, with the classical results of epistemic game theory as major high-lights. In this paper, we emphasize a recent new perspective toward “logical dynamics”, designing logical systems that focus on the [...] Read more.
Logic and game theory have had a few decades of contacts by now, with the classical results of epistemic game theory as major high-lights. In this paper, we emphasize a recent new perspective toward “logical dynamics”, designing logical systems that focus on the actions that change information, preference, and other driving forces of agency. We show how this dynamic turn works out for games, drawing on some recent advances in the literature. Our key examples are the long-term dynamics of information exchange, as well as the much-discussed issue of extensive game rationality. Our paper also proposes a new broader interpretation of what is happening here. The combination of logic and game theory provides a fine-grained perspective on information and interaction dynamics, and we are witnessing the birth of something new which is not just logic, nor just game theory, but rather a Theory of Play. Full article
(This article belongs to the Special Issue Epistemic Game Theory and Modal Logic)
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574 KiB  
Article
A Modal Logic of Epistemic Games
by Emiliano Lorini and François Schwarzentruber
Games 2010, 1(4), 478-526; https://doi.org/10.3390/g1040478 - 02 Nov 2010
Cited by 20 | Viewed by 10164
Abstract
We propose some variants of a multi-modal of joint action, preference and knowledge that support reasoning about epistemic games in strategic form. The first part of the paper deals with games with complete information. We first provide syntactic proofs of some well-known theorems [...] Read more.
We propose some variants of a multi-modal of joint action, preference and knowledge that support reasoning about epistemic games in strategic form. The first part of the paper deals with games with complete information. We first provide syntactic proofs of some well-known theorems in the area of interactive epistemology that specify some sufficient epistemic conditions of equilibrium notions such as Nash equilibrium and Iterated Deletion of Strictly Dominated Strategies (IDSDS). Then, we present a variant of the logic extended with dynamic operators of Dynamic Epistemic Logic (DEL). We show that it allows to express the notion IDSDS in a more compact way. The second part of the paper deals with games with weaker forms of complete information. We first discuss several assumptions on different aspects of perfect information about the game structure (e.g., the assumption that a player has perfect knowledge about the players’ strategy sets or about the preference orderings over strategy profiles), and show that every assumption is expressed by a corresponding logical axiom of our logic. Then we provide a proof of Harsanyi’s claim that all uncertainty about the structure of a game can be reduced to uncertainty about payoffs. Sound and complete axiomatizations of the logics are given, as well as some complexity results for the satisfiability problem. Full article
(This article belongs to the Special Issue Epistemic Game Theory and Modal Logic)
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224 KiB  
Article
Consistent Beliefs in Extensive Form Games
by Paulo Barelli
Games 2010, 1(4), 415-421; https://doi.org/10.3390/g1040415 - 20 Oct 2010
Cited by 1 | Viewed by 5837
Abstract
We introduce consistency of beliefs in the space of hierarchies of conditional beliefs (Battigalli and Siniscalchi) and use it to provide epistemic conditions for equilibria in finite multi-stage games with observed actions. Full article
(This article belongs to the Special Issue Epistemic Game Theory and Modal Logic)
224 KiB  
Article
The Role of Monotonicity in the Epistemic Analysis of Strategic Games
by Krzysztof R. Apt and Jonathan A. Zvesper
Games 2010, 1(4), 381-394; https://doi.org/10.3390/g1040381 - 08 Oct 2010
Cited by 11 | Viewed by 6095
Abstract
It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality [...] Read more.
It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to strengthen the above result to arbitrary games, other rationality notions, and transfinite iterations of the elimination process. We also clarify what conclusions one can draw for the customary dominance notions that are not monotonic. The main tool is Tarski’s Fixpoint Theorem. Full article
(This article belongs to the Special Issue Epistemic Game Theory and Modal Logic)
219 KiB  
Article
Backward Induction versus Forward Induction Reasoning
by Andres Perea
Games 2010, 1(3), 168-188; https://doi.org/10.3390/g1030168 - 02 Jul 2010
Cited by 15 | Viewed by 9674
Abstract
In this paper we want to shed some light on what we mean by backward induction and forward induction reasoning in dynamic games. To that purpose, we take the concepts of common belief in future rationality (Perea [1]) and extensive form rationalizability (Pearce [...] Read more.
In this paper we want to shed some light on what we mean by backward induction and forward induction reasoning in dynamic games. To that purpose, we take the concepts of common belief in future rationality (Perea [1]) and extensive form rationalizability (Pearce [2], Battigalli [3], Battigalli and Siniscalchi [4]) as possible representatives for backward induction and forward induction reasoning. We compare both concepts on a conceptual, epistemic and an algorithm level, thereby highlighting some of the crucial differences between backward and forward induction reasoning in dynamic games. Full article
(This article belongs to the Special Issue Epistemic Game Theory and Modal Logic)
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