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Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games

  • Battigalli, Pierpaolo
  • Siniscalchi, Marciano

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 88 (1999)
Issue (Month): 1 (September)
Pages: 188-230

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Handle: RePEc:eee:jetheo:v:88:y:1999:i:1:p:188-230
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
  2. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  3. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March.
  4. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
  5. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  6. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
  7. Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
  8. Werlang, Sérgio Ribeiro da Costa & Chin-Chiu Tan, Tommy, 1987. "The Bayesian Foundations of Solution Concepts of Games," Economics Working Papers (Ensaios Economicos da EPGE) 111, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  9. 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.
  10. Philip J. Reny, 1995. "Rational Behaviour in Extensive-Form Games," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 1-16, February.
  11. Battigalli, P. & Bonanno, G., 1993. "Synchronic Information and Common Knowledge in Extensive Games," Papers 93-11, California Davis - Institute of Governmental Affairs.
  12. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  13. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  14. Balkenborg, Dieter & Winter, Eyal, 1997. "A necessary and sufficient epistemic condition for playing backward induction," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 325-345, April.
  15. Ben-Porath, E., 1992. "Rationality, Nash Equilibrium and Backward Induction in Perfect Information Games," Papers 14-92, Tel Aviv - the Sackler Institute of Economic Studies.
  16. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  17. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Interactive beliefs, epistemic independence and strong rationalizability," Research in Economics, Elsevier, vol. 53(3), pages 247-273, September.
  18. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
  19. 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..
  20. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
  21. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  22. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  23. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
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