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Epistemic Logic and the Theory of Games and Decisions : THEORY AND DECISION LIBRARY SERIES C, GAME THEORY, MATHEMATICAL PROGRAMMING, AND OPERATIONS RESEARCH - Michael Bacharach

Epistemic Logic and the Theory of Games and Decisions

THEORY AND DECISION LIBRARY SERIES C, GAME THEORY, MATHEMATICAL PROGRAMMING, AND OPERATIONS RESEARCH

By: Michael Bacharach (Editor), Louis-Andre Gerard-Varet (Editor), Philippe Mongin (Editor), H.S. Shin (Editor)

Hardcover Published: December 2009
ISBN: 9780792348047
Number Of Pages: 366

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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.

Prefacep. vii
Contributing Authorsp. ix
Introductionp. xiii
Iterated Knowledge and Common Knowledge
On the Logic of Common Belief and Common Knowledgep. 3
A Complete Epistemic Logic for Multiple Agentsp. 35
Axiomatic Indefinability of Common Knowledge in Finitary Logicsp. 69
Eliminating Redundancies in Partition Spacesp. 95
The Logical Omniscience Problem
From Logical Omniscience to Partial Logical Competencep. 107
Knowledge and Belief Representation in a Partial Modelp. 129
Awareness and Partitional Informational Structuresp. 151
Representing the Knowledge of Turing Machinesp. 169
Applications to Game Theory and Decision Theory
Logics for Nonomniscient Agents: An Axiomatic Approachp. 193
Alternative Definitions of Knowledgep. 217
Synchronic Information, Knowledge and Common Knowledge in Extensive Gamesp. 235
Analyzing Games by Sequences of Metatheoriesp. 265
Rationally Justifiable Play and the Theory of Noncooperative Gamesp. 293
The Epistemic Structure of a Theory of a Gamep. 303
On the Evaluation of Solution Conceptsp. 345
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780792348047
ISBN-10: 0792348044
Series: THEORY AND DECISION LIBRARY SERIES C, GAME THEORY, MATHEMATICAL PROGRAMMING, AND OPERATIONS RESEARCH
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 366
Published: December 2009
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 3.18
Weight (kg): 0.74