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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.

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  • 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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    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, 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 164, University of California, Davis, Department of Economics.
    4. Giacomo Bonanno, 2005. "Temporal interaction of information and belief," Working Papers 541, University of California, Davis, Department of Economics.
    5. Giacomo Bonanno, 2012. "Epistemic foundations of game theory," Working Papers 70, University of California, Davis, Department of Economics.
    6. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 45, University of California, Davis, Department of Economics.
    7. Holliday, Wesley H., 2025. "A partial-state space model of unawareness," Journal of Mathematical Economics, Elsevier, vol. 116(C).
    8. Vanessa de Sousa Duarte & Miguel Rocha de Sousa, 2021. "Lessons from the Portuguese Carnations Revolution of 1974 by a game theory approach," CEFAGE-UE Working Papers 2021_2022, University of Evora, CEFAGE-UE (Portugal).
    9. Antoine Billot & Jean-Christophe Vergnaud & Bernard Walliser, 2008. "Multiplayer belief revision," Post-Print halshs-00344461, HAL.
    10. Wesley H. Holliday, 2024. "A partial-state space model of unawareness," Papers 2412.00897, arXiv.org, revised Dec 2024.
    11. Oliver Board, 2002. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Working Paper 244, Department of Economics, University of Pittsburgh, revised Jan 2002.
    12. Billot, Antoine & Vergnaud, Jean-Christophe & Walliser, Bernard, 2015. "Multiagent belief revision," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 47-57.
    13. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.
    14. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    15. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 6, University of California, Davis, Department of Economics.
    16. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    17. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 134, University of California, Davis, Department of Economics.
    18. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 24, University of California, Davis, Department of Economics.
    19. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 45, University of California, Davis, Department of Economics.
    20. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 209, University of California, Davis, Department of Economics.
    21. 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, vol. 2014(113), pages 5-33.
    22. Áron Tóbiás, 2021. "Meet meets join: the interaction between pooled and common knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 989-1019, December.
    23. Giacomo Bonanno, 2005. "Temporal interaction of information and belief," Working Papers 141, University of California, Davis, Department of Economics.
    24. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 76, University of California, Davis, Department of Economics.

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    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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