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Dynamic interactive epistemology

  • Board, Oliver

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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 49 (2004)
Issue (Month): 1 (October)
Pages: 49-80

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Handle: RePEc:eee:gamebe:v:49:y:2004:i:1:p:49-80
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. D. Samet, 1987. "Ignoring Ignorance and Agreeing to Disagree," Discussion Papers 749, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Oliver Board, 2003. "The Not-So-Absent-Minded Driver," Economics Series Working Papers 147, University of Oxford, Department of Economics.
  3. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
  4. 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, June.
  5. 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.
  6. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  7. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  8. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
  9. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  10. Oliver Board, 2003. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Economics Series Working Papers 148, University of Oxford, Department of Economics.
  11. Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  12. 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.
  13. 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, vol. 28(3), pages 331-365.
  14. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  15. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
  16. Geanakoplos, John & Pearce, David & Stacchetti, Ennio, 1989. "Psychological games and sequential rationality," Games and Economic Behavior, Elsevier, vol. 1(1), pages 60-79, March.
  17. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
  18. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
  19. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  20. 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.
  21. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  22. 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.
  23. 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.
  24. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
  25. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
  26. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  27. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee.
  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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