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Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games

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  • Battigalli, Pierpaolo
  • Siniscalchi, Marciano

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. 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).
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  4. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  5. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  6. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
  7. Roger B. Myerson, 1984. "Multistage Games with Communication," Discussion Papers 590, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  9. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  10. Ben-Porath, Elchanan, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Wiley Blackwell, vol. 64(1), pages 23-46, January.
  11. Battigalli, P. & Bonanno, G., 1993. "Synchronic Information and Common Knowledge in Extensive Games," Papers 93-11, California Davis - Institute of Governmental Affairs.
  12. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
  13. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
  14. Philip J. Reny, 1995. "Rational Behaviour in Extensive-Form Games," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 1-16, February.
  15. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Interactive beliefs, epistemic independence and strong rationalizability," Research in Economics, Elsevier, vol. 53(3), pages 247-273, September.
  16. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  17. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
  18. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
  19. Balkenborg, Dieter & Eyal Winter, 1995. "A Necessary and Sufficient Epistemic Condition for Playing Backward Induction," Discussion Paper Serie B 331, University of Bonn, Germany.
  20. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  21. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
  22. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
  23. 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.
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