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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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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 125.

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Date of creation: 01 Nov 2002
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Handle: RePEc:oxf:wpaper:125

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Keywords: interactive epistemology; belief revision; semantic; syntactic;

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References

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  1. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
  2. Board, Oliver, 2003. "The not-so-absent-minded driver," Research in Economics, Elsevier, vol. 57(3), pages 189-200, September.
  3. Oliver Board, 2002. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Working Papers 244, University of Pittsburgh, Department of Economics, revised Jan 2002.
  4. Giacomo Bonanno & Pierpaolo Battigalli, 2003. "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Working Papers 9814, University of California, Davis, Department of Economics.
  5. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
  6. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  7. D. Samet, 1987. "Ignoring Ignorance and Agreeing to Disagree," Discussion Papers 749, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  9. 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.
  10. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
  11. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  12. 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.
  13. 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.
  14. 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.
  15. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
  16. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  17. Geanakoplos, John & Pearce, David & Stacchetti, Ennio, 1989. "Psychological games and sequential rationality," Games and Economic Behavior, Elsevier, vol. 1(1), pages 60-79, March.
  18. Ronald Fagin & John Geanakoplos & Joseph Y. Halpern & Moshe Y. Vardi, 1999. "The Hierarchical Approach to Modeling Knowledge and Common Knowledge," Cowles Foundation Discussion Papers 1213, Cowles Foundation for Research in Economics, Yale University.
  19. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May.
  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. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee.
  22. Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  23. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
  24. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
  25. 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.
  26. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
  27. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  28. Dufwenberg, Martin, 2002. "Marital investments, time consistency and emotions," Journal of Economic Behavior & Organization, Elsevier, vol. 48(1), pages 57-69, May.
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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 52-86, February.
  2. repec:hal:journl:halshs-00344461 is not listed on IDEAS
  3. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
  4. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 76, University of California, Davis, Department of Economics.
  5. Giacomo Bonanno, 2005. "A simple modal logic for belief revision," Working Papers 517, 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. 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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