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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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  2. Board, Oliver, 2003. "The not-so-absent-minded driver," Research in Economics, Elsevier, vol. 57(3), pages 189-200, September.
  3. In-Koo Cho & David M. Kreps, 1997. "Signaling Games and Stable Equilibria," Levine's Working Paper Archive 896, David K. Levine.
  4. 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.
  5. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  6. Rubinstein, Ariel, 1995. "On the Interpretation of Decision Problems with Imperfect Recall," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 324-324, December.
  7. Geanakoplos, John & Pearce, David & Stacchetti, Ennio, 1989. "Psychological games and sequential rationality," Games and Economic Behavior, Elsevier, vol. 1(1), pages 60-79, March.
  8. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
  9. 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.
  10. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
  11. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
  12. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee.
  13. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
  14. 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.
  15. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
  16. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
  17. Oliver Board, 2003. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Economics Series Working Papers 148, University of Oxford, Department of Economics.
  18. Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  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, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
  22. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  23. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  24. 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.
  25. 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.
  26. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  27. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
  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. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner’s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.
  2. Oliver Board, 2002. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Working Papers 244, University of Pittsburgh, Department of Economics, revised Jan 2002.
  3. Giacomo Bonanno, 2014. "Reasoning about strategies and rational play in dynamic games," Working Papers 149, University of California, Davis, Department of Economics.
  4. Giacomo Bonanno, 2005. "A simple modal logic for belief revision," Working Papers 517, University of California, Davis, Department of Economics.
  5. repec:hal:journl:halshs-00344461 is not listed on IDEAS
  6. 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.
  7. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 76, University of California, Davis, Department of Economics.

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