Epistemic Logic and the Theory of Games and Decisions

This book arose out of a conference on "Epistemic Logic and the Theory of Games and Decisions" that took place in January 1994 at the Centre Inter national de Recherches Mathematiques in Marseille. The convergence of game theory and epistemic logic has been in progress for two decades. The aim of the conference was to explore this rapprochement further by gathering spe cialists from different professional communities, i. e. , economics, mathematics, philosophy, and computer science. Also, the organizors aimed at fostering the work centered on the issues of knowledge and belief that has recently been pursued amongst game theorists and decision theorists. The conference was funded by the following institutions: Centre National de la Recherche Sci entifique (France), Ministere de l'Enseignement Superieur et de la Recherche (France), Association pour Ie Developpement de la Recherche en Economie et Statistique (France). It was also supported by the Human Capital and Mobility Programme of the EU, as well as, locally, by the Ville de Marseille. We would like to express our gratitude to these institutions for their generous help. Despite the success of the conference, it was not the editors' intention to circulate just another volume of proceedings in the usual style. Throughout the more than two-year editorial process, they have pursued the goal of providing a no doubt non-exhaustive, but hopefully thorough and accurate, state of the art account of a promising field of research.

Klappentext

The convergence of game theory and epistemic logic has been in progress for two decades and this book explores this further by gathering specialists from different professional communities, i.e., economics, mathematics, philosophy, and computer science. This volume considers the issues of knowledge, belief and strategic interaction, with each contribution evaluating the foundational issues. In particular, emphasis is placed on epistemic logic and the representative topics of backward induction arguments and syntax/semantics and the logical omniscience problem. Part I of this collection deals with iterated knowledge in the multi-agent context, and more particularly with common knowledge. The first two papers in Part II of the collection address the so-called logical omniscience problem, a problem which has attracted much attention in the recent epistemic logic literature, and is pertinent to some of the issues discussed by decision theorists under the heading `bounded rationality'. The remaining two chapters of section II provide two quite different angles on the strength of S5 (or the partitional model of information)- and so two different reasons for eschewing the strong form of logical omniscience implicit in S5. Part III gives attention to application to game theory and decision theory.

Inhalt
I Iterated Knowledge and Common Knowledge.- 1 On the Logic of Common Belief and Common Knowledge.- 2 A Complete Epistemic Logic for Multiple Agents.- 3 Axiomatic Indefinability of Common Knowledge in Finitary Logics.- 4 Eliminating Redundancies in Partition Spaces.- II The Logical Omniscience Problem.- 5 From Logical Omniscience to Partial Logical Competence.- 6 Knowledge and Belief Representation in a Partial Model.- 7 Awareness and Partitional Informational Structures.- 8 Representing the Knowledge of Turing Machines.- III Applications to Game Theory and Decision Theory.- 9 Logics for Nonomniscient Agents: An Axiomatic Approach.- 10 Alternative Definitions of Knowledge.- 11 Synchronic Information, Knowledge and Common Knowledge in Extensive Games.- 12 Analyzing Games by Sequences of Metatheories.- 13 Rationally Justifiable Play and the Theory of Noncooperative Games.- 14 The Epistemic Structure of a Theory of a Game.- 15 On the Evaluation of Solution Concepts.