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Epistemic logics and their game theoretic applications: Introduction

Author

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  • Mamoru Kaneko

    () (Institute of Policy and Planning Sciences, University of Tsukuba, Ibaraki 305-8573, JAPAN)

Abstract

This paper is written as an introduction to epistemic logics and their game theoretic applications. It starts with both semantics and syntax of classical logic, and goes to the Hilbert-style proof-theory and Kripke-style model theory of epistemic logics. In these theories, we discuss individual decision making in some simple game examples. In particular, we will discuss the distinction between beliefs and knowledge, and how false beliefs play roles in game theoretic decision making. Finally, we discuss extensions of epistemic logics to incorporate common knowledge. In the extension, we discuss also false beliefs on common knowledge.

Suggested Citation

  • Mamoru Kaneko, 2002. "Epistemic logics and their game theoretic applications: Introduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(1), pages 7-62.
  • Handle: RePEc:spr:joecth:v:19:y:2002:i:1:p:7-62
    Note: Received: July 1, 2000; revised version: April 19, 2001
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    Cited by:

    1. Kaneko, Mamoru & Kline, J. Jude, 2008. "Inductive game theory: A basic scenario," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1332-1363, December.
    2. Xiao Luo, 2009. "On the foundation of stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 185-201, August.

    More about this item

    Keywords

    Classical logic; Epistemic logic; Common knowledge logic; Beliefs; Knowledge; Dominant strategy; Decision criterion; Epistemic depth of a formula.;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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