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Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games

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Pierpaolo Battigalli

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Abstract

We show how to extend the construction of infinite hierachies of beliefs (Mertens and Zamir (1985), Brandenburger and Dekel (1993)) from the case of probability measures to the case of conditional probability systems (CPSs) defined with respect to a fixed collection of relevant hypotheses. The set of hierarchies of CPSs satisfying common certainty of coherency conditional on every relevant hypothesis corresponds to a universal type space. This construction provides a unified framework to analyze the epistemic foundations of solution concepts for dynamic games. As an illustration, we derive some results about conditional common certainty of rationality and rationalizability in multistage games with observed actions.

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Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 111.

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Handle: RePEc:igi:igierp:111

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  1. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April. [Downloadable!] (restricted)
  2. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996. [Downloadable!]
  3. Philip J. Reny, 1995. "Rational Behaviour in Extensive-Form Games," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 1-16, February. [Downloadable!] (restricted)
  4. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  7. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August. [Downloadable!] (restricted)
  8. Battigalli, P. & Bonanno, G., 1993. "Synchronic Information and Common Knowledge in Extensive Games," Papers 93-11, California Davis - Institute of Governmental Affairs.
  9. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March. [Downloadable!] (restricted)
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  10. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February. [Downloadable!] (restricted)
  11. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Joseph Greenberg & Sudheer Gupta & Xiao Luo, 2009. "Mutually acceptable courses of action," Economic Theory, Springer, vol. 40(1), pages 91-112, July. [Downloadable!] (restricted)
  2. Perea,Andrés, 2004. "Minimal Belief Revision leads to Backward Induction," Research Memoranda 032, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  3. Jeffrey C. Ely & Marcin Peski, 2005. "Hierarchies of Belief and Interim Rationalizability," Levine's Bibliography 122247000000000817, UCLA Department of Economics. [Downloadable!]
    Other versions:
  4. Oliver Board, 2002. "Algorithmic Characterization of Rationalizability in Extensive Form Games," Working Papers 244, University of Pittsburgh, Department of Economics, revised Jan 2002. [Downloadable!]
    Other versions:
  5. Amanda Friedenberg, 2006. "Can Hidden Variables Explain Correlation? (joint with Adam Brandenburger)," Theory workshop papers 815595000000000005, UCLA Department of Economics. [Downloadable!]
  6. Pierpaolo Battigalli & Marciano Siniscalchi, . "An Epistemic Characterisation of Extensive Form Rationalisability," Working Papers 1999.25, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
  7. Vittorio Pelligra, 2007. "Intentions, Trust and Frames: A note on Sociality and the Theory of Games," Working Paper CRENoS 200702, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia. [Downloadable!]
  8. repec:bep:theadv:v:3:y:2003:i:1:p:1073-1073 is not listed on IDEAS
  9. Oliver Board, 2002. "Dynamic Interactive Epistemology," Economics Series Working Papers 125, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  10. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers 9817a118e65062903de7c3577, David K. Levine. [Downloadable!]
  11. Andrés Perea, 2006. "Proper belief revision and rationalizability in dynamic games," International Journal of Game Theory, Springer, vol. 34(4), pages 529-559, November. [Downloadable!] (restricted)
  12. Pierpaolo Battigalli & Martin Dufwenberg, 2005. "Dynamic Psychological Games," Working Papers 287, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
    Other versions:
  13. Asheim,G.B., 1999. "On the epistemic foundation for backward induction," Memorandum 30/1999, Oslo University, Department of Economics. [Downloadable!]
    Other versions:
  14. Pierpaolo Battigalli, 2004. "Rationalization in Signaling Games: Theory and Applications," Working Papers 275, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
    Other versions:
  15. Perea,Andrés, 2003. "Proper Rationalizability and Belief Revision in Dynamic Games," Research Memoranda 048, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  16. Penta, Antonio, 2004. "Perfect Sequential Reciprocity and Dynamic Consistency," MPRA Paper 10261, University Library of Munich, Germany, revised Sep 2007. [Downloadable!]
  17. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer, vol. 35(4), pages 465-492, April. [Downloadable!] (restricted)
  18. Muhamet Yildiz & Jonathan Weinsten, 2004. "Impact of higher-order uncertainty," Econometric Society 2004 North American Winter Meetings 157, Econometric Society. [Downloadable!]
    Other versions:
  19. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002. [Downloadable!]
  20. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics. [Downloadable!]
    Other versions:
  21. Licun Xue, . "A Notion of Consistent Rationalizability - Between Weak and Pearce's Extensive Form Rationalizability," Economics Working Papers 2000-4, School of Economics and Management, University of Aarhus. [Downloadable!]
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