Epistemic Logic and the Theory of Games and Decisions / Edition 1

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Overview

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.
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Editorial Reviews

Booknews
Furthers the convergence of the two fields over the past two decades by gathering specialists from economics, mathematics, philosophy, and computer science to evaluation the foundational issues underlying knowledge, belief, and strategic interaction. They emphasize epistemic logic and the representative topics of backward induction arguments, and syntax and semantics in the logical omniscience problem. The core of the 15 papers were presented at a January 1994 conference in Marseilles, but others have been added to flesh out a thorough and accurate accounting of the field of research; all have been refereed and revised at several stages. Among the topics are the logic of common belief and common knowledge, awareness and partitioned informational structures, an axiomatic approach to logics for non- omniscient agents, and analyzing games by sequences of metatheories. No index. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780792348047
  • Publisher: Springer US
  • Publication date: 10/31/1997
  • Series: Theory and Decision Library C Series , #20
  • Edition description: 1997
  • Edition number: 1
  • Pages: 366
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.94 (d)

Table of Contents

Preface
Contributing Authors
Introduction
1 On the Logic of Common Belief and Common Knowledge 3
2 A Complete Epistemic Logic for Multiple Agents 35
3 Axiomatic Indefinability of Common Knowledge in Finitary Logics 69
4 Eliminating Redundancies in Partition Spaces 95
5 From Logical Omniscience to Partial Logical Competence 107
6 Knowledge and Belief Representation in a Partial Model 129
7 Awareness and Partitional Informational Structures 151
8 Representing the Knowledge of Turing Machines 169
9 Logics for Nonomniscient Agents: An Axiomatic Approach 193
10 Alternative Definitions of Knowledge 217
11 Synchronic Information, Knowledge and Common Knowledge in Extensive Games 235
12 Analyzing Games by Sequences of Metatheories 265
13 Rationally Justifiable Play and the Theory of Noncooperative Games 293
14 The Epistemic Structure of a Theory of a Game 303
15 On the Evaluation of Solution Concepts 345
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