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A structure theorem for rationalizability in the normal form of dynamic games

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  • Chen, Yi-Chun

Abstract

We prove that the structure theorem for rationalizability originally from Weinstein and Yildiz (2007) applies to any finite extensive-form game with perfect recall and suitably rich payoffs. We demonstrate that the ties induced by the extensive form do not change the result of Weinstein and Yildiz (2007). Specifically, like Weinstein and Yildiz (2007), we adopt the normal-form concept of interim correlated rationalizability and we assume that players have no relevant knowledge of the extensive-form payoff structure. The extensive-form result is weaker in the sense that while the result of Weinstein and Yildiz (2007) does not depend on the latter assumption, our result does. Our result implies that without restrictions on playersʼ knowledge of payoffs, the dynamic structure of extensive-form games offers no force for robust refinements of rationalizability. We also strengthen the main selection result of Weinstein and Yildiz (2007) by showing that the result holds for any (not necessarily finite) type.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 75 (2012)
Issue (Month): 2 ()
Pages: 587-597

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Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:587-597

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

Related research

Keywords: Rationalizability; Incomplete information; Robustness; Universal type space; Higher-order beliefs; Extensive-form games;

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References

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  1. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, 03.
  2. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  3. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
  4. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  5. Fudenberg, Drew & Kreps, David M. & Levine, David K., 1988. "On the robustness of equilibrium refinements," Journal of Economic Theory, Elsevier, vol. 44(2), pages 354-380, April.
  6. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
  7. 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.
  8. David M. Frankel & Stephen Morris & Ady Pauzner, 2000. "Equilibrium Selection in Global Games with Strategic Complementarities," Econometric Society World Congress 2000 Contributed Papers 1490, Econometric Society.
  9. Stephen Morris & Hyun Song Shin, 2007. "Common Belief Foundations of Global Games," Levine's Bibliography 122247000000001638, UCLA Department of Economics.
  10. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on types," Theoretical Economics, Econometric Society, vol. 1(3), pages 275-309, September.
  11. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
  12. Weinstein, Jonathan & Yildiz, Muhamet, 2011. "Sensitivity of equilibrium behavior to higher-order beliefs in nice games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 288-300, May.
  13. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
  14. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Cited by:
  1. Penta, Antonio, 2013. "On the structure of rationalizability for arbitrary spaces of uncertainty," Theoretical Economics, Econometric Society, vol. 8(2), May.
  2. Zaki Wahhaj, 2012. "Social Norms, Higher-Order Beliefs and the Emperor's New Clothes," Studies in Economics 1210, Department of Economics, University of Kent.

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