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Dynamic Interactive Epistemology

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  • Oliver Board

Abstract

The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various game-theoretic solution concepts. Much of this work is based around the (static) Aumann structure model of interactive epistemology, but more recently dynamic models of interactive reasoning have been developed, most notably by Stalnaker[39] and Battigalli and Siniscalchi [6], and used to analyze rational play in extensive form games. But while the properties of Kripke structures are well understood, without a formal language in which belief and belief revision statements can be expressed, it is unclear exactly what are the properties of these dynamic models. Here we investigate this question, by defining such a language. A semantics and syntax are presented, with soundness and completeness theorems linking the two.

Suggested Citation

  • Oliver Board, 2002. "Dynamic Interactive Epistemology," Economics Series Working Papers 125, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:125
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    File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper125.pdf
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    References listed on IDEAS

    as
    1. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, pages 149-225.
    2. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
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    6. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
    7. Board, Oliver, 2003. "The not-so-absent-minded driver," Research in Economics, Elsevier, pages 189-200.
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    9. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, pages 188-230.
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    11. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
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    26. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
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    Citations

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    Cited by:

    1. Johan Van Benthem & Eric Pacuit & Olivier Roy, 2011. "Toward a Theory of Play: A Logical Perspective on Games and Interaction," Games, MDPI, Open Access Journal, vol. 2(1), pages 1-35, February.
    2. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    3. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 45, University of California, Davis, Department of Economics.
    4. repec:pit:wpaper:244 is not listed on IDEAS
    5. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 136, University of California, Davis, Department of Economics.
    6. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.
    7. Billot, Antoine & Vergnaud, Jean-Christophe & Walliser, Bernard, 2015. "Multiagent belief revision," Journal of Mathematical Economics, Elsevier, pages 47-57.
    8. Guilhem Lecouteux, 2017. "Bayesian Game Theorists and Non-Bayesian Players," GREDEG Working Papers 2017-30, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis.
    9. repec:hal:journl:halshs-00344461 is not listed on IDEAS
    10. Amedeo Fossati, 2014. "The Luigi Einaudi vs. Mauro Fasiani epistemological debate (1938-1943): the end of the italian tradition in Public Finance," STUDI ECONOMICI, FrancoAngeli Editore, pages 5-33.
    11. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 76, University of California, Davis, Department of Economics.
    12. Guilhem Lecouteux, 2017. "Bayesian Game Theorists and non-Bayesian Players," Working Papers halshs-01633126, HAL.

    More about this item

    Keywords

    interactive epistemology; belief revision; semantic; syntactic;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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