research-article

A logical characterization of iterated admissibility

Authors:

Joseph Y. Halpern,

Rafael PassAuthors Info & Claims

TARK '09: Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge

Pages 146 - 155

https://doi.org/10.1145/1562814.1562836

Published: 06 July 2009 Publication History

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Abstract

Brandenburger, Friedenberg, and Keisler provide an epistemic characterization of iterated admissibility (i.e., iterated deletion of weakly dominated strategies) where uncertainty is represented using LPSs (lexicographic probability sequences). Their characterization holds in a rich structure called a complete structure, where all types are possible. Here, a logical characterization of iterated admissibility is given that involves only standard probability and holds in all structures, not just complete structures. Roughly speaking, our characterization shows that iterated admissibility captures the intuition that "all the agent knows" is that agents satisfy the appropriate rationality assumptions.

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Cited By

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Keisler HLee B(2023)Common assumption of rationalityJournal of Mathematical Economics10.1016/j.jmateco.2023.102892109(102892)Online publication date: Dec-2023
https://doi.org/10.1016/j.jmateco.2023.102892
Liu DFeng Q(2023)On the Progression of BeliefArtificial Intelligence10.1016/j.artint.2023.103947(103947)Online publication date: May-2023
https://doi.org/10.1016/j.artint.2023.103947
(2019)Semantical considerations on multiagent only knowingArtificial Intelligence10.5555/2781920.2782452223:C(1-26)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.5555/2781920.2782452
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Index Terms

A logical characterization of iterated admissibility
1. Computing methodologies
  1. Artificial intelligence
    1. Distributed artificial intelligence
    2. Knowledge representation and reasoning
      1. Probabilistic reasoning
      2. Vagueness and fuzzy logic
  2. Modeling and simulation
    1. Model development and analysis
      1. Modeling methodologies
2. Theory of computation
  1. Logic

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Published In

TARK '09: Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge

July 2009

272 pages

ISBN:9781605585604

DOI:10.1145/1562814

Program Chair:
Aviad Heifetz
The Open University of Israel

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Association for Computing Machinery

New York, NY, United States

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Published: 06 July 2009

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TARK '09: The 11th conference on Theoretical aspects of rationality and knowledge

July 6 - 8, 2009

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TARK '09 Paper Acceptance Rate 29 of 77 submissions, 38%;

Overall Acceptance Rate 61 of 177 submissions, 34%

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Keisler HLee B(2023)Common assumption of rationalityJournal of Mathematical Economics10.1016/j.jmateco.2023.102892109(102892)Online publication date: Dec-2023
https://doi.org/10.1016/j.jmateco.2023.102892
Liu DFeng Q(2023)On the Progression of BeliefArtificial Intelligence10.1016/j.artint.2023.103947(103947)Online publication date: May-2023
https://doi.org/10.1016/j.artint.2023.103947
(2019)Semantical considerations on multiagent only knowingArtificial Intelligence10.5555/2781920.2782452223:C(1-26)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.5555/2781920.2782452
Halpern JPass R(2019)A Conceptually Well-Founded Characterization of Iterated Admissibility Using an "All I Know" OperatorElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.297.15297(221-232)Online publication date: 19-Jul-2019
https://doi.org/10.4204/EPTCS.297.15
Barbero F(2018)Cooperation in Games and Epistemic Readings of Independence-Friendly SentencesJournal of Logic, Language and Information10.1007/s10849-017-9255-126:3(221-260)Online publication date: 24-Dec-2018
https://dl.acm.org/doi/10.1007/s10849-017-9255-1
Belle VLakemeyer G(2017)Reasoning about probabilities in unbounded first-order dynamical domainsProceedings of the 26th International Joint Conference on Artificial Intelligence10.5555/3171642.3171761(828-836)Online publication date: 19-Aug-2017
https://dl.acm.org/doi/10.5555/3171642.3171761
Bjorndahl AHalpern J(2017)From Type Spaces to Probability Frames and Back, via LanguageElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.251.6251(75-87)Online publication date: 25-Jul-2017
https://doi.org/10.4204/EPTCS.251.6
Pacuit E(2016)Dynamic Models of Rational Deliberation in GamesModels of Strategic Reasoning10.1007/978-3-662-48540-8_1(3-33)Online publication date: 9-Jan-2016
https://doi.org/10.1007/978-3-662-48540-8_1
Pacuit ERoy O(2016)A Dynamic Analysis of Interactive RationalityEpistemology, Knowledge and the Impact of Interaction10.1007/978-3-319-26506-3_6(187-206)Online publication date: 29-Apr-2016
https://doi.org/10.1007/978-3-319-26506-3_6
Lorini E(2015)A minimal logic for interactive epistemologySynthese10.1007/s11229-015-0960-5193:3(725-755)Online publication date: 15-Dec-2015
https://doi.org/10.1007/s11229-015-0960-5
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A Logical Characterisation of Static Equivalence

Characterizations of iterated admissibility based on PEGL

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A Logical Characterisation of Static Equivalence

Characterizations of iterated admissibility based on PEGL

A spatial logical characterisation of context bisimulation

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