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On the generic robustness of solution concepts to incomplete information


  • Carmona, Guilherme


We consider the generic robustness of an upper hemi-continuous solution concept on a class of games of interest which has been embedded in a larger space of games. We show that generic robustness follows if the class of games of interest is “large” relative to the class of games in which it has been embedded. This result is used to show why interim correlated rationalizable actions are generically robust to players’ hierarchies of beliefs as established by Weinstein and Yildiz (2007) even without their richness condition. It is also used to provide a formal sense according to which, in the setting of Kajii and Morris (1997b), the set of representations of a complete information game is small in the space of incomplete information games in which it is embedded. This difference in relative sizes makes the robustness problems of Kajii and Morris (1997b) and Weinstein and Yildiz (2007) be incomparable and helps explaining why their conclusions differ so significantly.

Suggested Citation

  • Carmona, Guilherme, 2018. "On the generic robustness of solution concepts to incomplete information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 13-18.
  • Handle: RePEc:eee:mateco:v:75:y:2018:i:c:p:13-18
    DOI: 10.1016/j.jmateco.2017.12.003

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    References listed on IDEAS

    1. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    2. Yi‐Chun Chen & Siyang Xiong, 2013. "Genericity and Robustness of Full Surplus Extraction," Econometrica, Econometric Society, vol. 81(2), pages 825-847, March.
    3. 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..
    4. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, March.
    5. 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, March.
    6. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    7. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," CORE Discussion Papers RP 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    9. Weinstein, Jonathan & Yildiz, Muhamet, 2017. "Interim correlated rationalizability in infinite games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 82-87.
    10. Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, vol. 71(4), pages 1255-1267, July.
    11. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    12. Chen, Yi-Chun, 2012. "A structure theorem for rationalizability in the normal form of dynamic games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 587-597.
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    Cited by:

    1. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.


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