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Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games

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  • Pierpaolo Battigalli

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. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 60(3), pages 627-49, May.
  2. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(1), pages 92-100, August.
  3. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 189-198, February.
  4. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, Econometric Society, vol. 54(2), pages 323-58, March.
  5. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, Elsevier, vol. 36(1), pages 31-56, July.
  6. Balkenborg, Dieter & Eyal Winter, 1995. "A Necessary and Sufficient Epistemic Condition for Playing Backward Induction," Discussion Paper Serie B, University of Bonn, Germany 331, University of Bonn, Germany.
  7. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  8. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, Elsevier, vol. 74(1), pages 40-61, May.
  9. Battigalli, P. & Bonanno, G., 1993. "Synchronic Information and Common Knowledge in Extensive Games," Papers, California Davis - Institute of Governmental Affairs 93-11, California Davis - Institute of Governmental Affairs.
  10. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(2), pages 257-274, April.
  11. 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).
  12. Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information, EconWPA 9408001, EconWPA, revised 17 Aug 1994.
  13. Philip J. Reny, 1995. "Rational Behaviour in Extensive-Form Games," Canadian Journal of Economics, Canadian Economics Association, Canadian Economics Association, vol. 28(1), pages 1-16, February.
  14. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 1029-50, July.
  15. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information, EconWPA 9609002, EconWPA, revised 17 Sep 1996.
  16. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Interactive beliefs, epistemic independence and strong rationalizability," Research in Economics, Elsevier, Elsevier, vol. 53(3), pages 247-273, September.
  17. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, Elsevier, vol. 17(1), pages 138-146, November.
  18. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, Elsevier, vol. 17(1), pages 135-137, November.
  19. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, Elsevier, vol. 13(2), pages 178-200, April.
  20. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, 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, Elsevier, vol. 8(1), pages 6-19.
  22. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
  23. Ben-Porath, Elchanan, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 64(1), pages 23-46, January.
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