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Dynamic interactive epistemology

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  • Board, Oliver

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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  • Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    • Handle: RePEc:eee:gamebe:v:49:y:2004:i:1:p:49-80
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    1. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    2. Oliver Board, 2002. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Working Paper 244, Department of Economics, University of Pittsburgh, revised Jan 2002.
    3. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    4. 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..
    5. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    6. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    7. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819.
    8. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, December.
    9. Board, Oliver, 2003. "The not-so-absent-minded driver," Research in Economics, Elsevier, vol. 57(3), pages 189-200, September.
    10. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July.
    11. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    12. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
    13. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
    14. John Geanakoplos & (**), Moshe Y. Vardi & Joseph Y. Halpern & Ronald Fagin, 1999. "The hierarchical approach to modeling knowledge and common knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 331-365.
    15. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, vol. 59(2), pages 257-274, April.
    16. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    17. Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 23-46.
    18. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(2), pages 133-163, October.
    19. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833.
    20. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    21. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
    22. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
    23. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
    24. Oliver Board, 2002. "The Deception of the Greeks: Generalizing the Information Structure of Extensive Form Games," Economics Series Working Papers 137, University of Oxford, Department of Economics.
    25. Geanakoplos, John & Pearce, David & Stacchetti, Ennio, 1989. "Psychological games and sequential rationality," Games and Economic Behavior, Elsevier, vol. 1(1), pages 60-79, March.
    26. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    27. Kohlberg, Elon & Reny, Philip J., 1997. "Independence on Relative Probability Spaces and Consistent Assessments in Game Trees," Journal of Economic Theory, Elsevier, vol. 75(2), pages 280-313, August.
    28. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    29. Dufwenberg, Martin, 2002. "Marital investments, time consistency and emotions," Journal of Economic Behavior & Organization, Elsevier, vol. 48(1), pages 57-69, May.
    30. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826.
    31. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
    32. Oliver Board, 2003. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Economics Series Working Papers 148, University of Oxford, Department of Economics.
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    Citations

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    Cited by:

    1. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 164, University of California, Davis, Department of Economics.
    2. Giacomo Bonanno, 2005. "Temporal interaction of information and belief," Working Papers 541, University of California, Davis, Department of Economics.
    3. Oliver Board, 2002. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Working Paper 244, Department of Economics, University of Pittsburgh, revised Jan 2002.
    4. 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.
    5. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 209, University of California, Davis, Department of Economics.
    6. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 11, University of California, Davis, Department of Economics.
    7. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 45, University of California, Davis, Department of Economics.
    8. Billot, Antoine & Vergnaud, Jean-Christophe & Walliser, Bernard, 2015. "Multiagent belief revision," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 47-57.
    9. Giacomo Bonanno, 2012. "Epistemic foundations of game theory," Working Papers 70, University of California, Davis, Department of Economics.
    10. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 6, University of California, Davis, Department of Economics.
    11. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 134, University of California, Davis, Department of Economics.
    12. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    13. 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.
    14. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 45, University of California, Davis, Department of Economics.
    15. 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.
    16. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    17. Antoine Billot & Jean-Christophe Vergnaud & Bernard Walliser, 2008. "Multiplayer belief revision," Post-Print halshs-00344461, HAL.
    18. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner?s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.
    19. 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.
    20. Giacomo Bonanno, 2005. "Temporal interaction of information and belief," Working Papers 141, University of California, Davis, Department of Economics.
    21. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 76, University of California, Davis, Department of Economics.

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    More about this item

    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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