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Incomplete Information Robustness

Author

Listed:
  • Stephen Morris
  • Takashi Ui

Abstract

Consider an analyst who models a strategic situation using an incomplete information game. The true game may involve correlated, duplicated belief hierarchies, but the analyst lacks knowledge of the correlation structure and can only approximate each belief hierarchy. To make predictions in this setting, the analyst uses belief-invariant Bayes correlated equilibria (BIBCE) and seeks to determine which one is justifiable. We address this question by introducing the notion of robustness: a BIBCE is robust if, for every nearby incomplete information game, there exists a BIBCE close to it. Our main result provides a sufficient condition for robustness using a generalized potential function. In a supermodular potential game, a robust BIBCE is a Bayes Nash equilibrium, whereas this need not hold in other classes of games.

Suggested Citation

  • Stephen Morris & Takashi Ui, 2025. "Incomplete Information Robustness," Papers 2502.19075, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2502.19075
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    References listed on IDEAS

    as
    1. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-1380, September.
    2. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    3. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    4. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    5. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    6. Pram, Kym, 2019. "On the equivalence of robustness to canonical and general elaborations," Journal of Economic Theory, Elsevier, vol. 180(C), pages 1-10.
    7. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    8. Atsushi Kajii & Stephen Morris, 2020. "Correction to: Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(2), pages 353-354, April.
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    10. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    11. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    12. Atsushi Kajii & Stephen Morris, 2020. "Refinements and higher-order beliefs: a unified survey," The Japanese Economic Review, Springer, vol. 71(1), pages 7-34, January.
    13. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    14. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    15. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    16. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    18. Satoru Takahashi, 2020. "Non-equivalence between all and canonical elaborations," The Japanese Economic Review, Springer, vol. 71(1), pages 43-57, January.
    19. Daisuke Oyama & Satoru Takahashi, 2020. "Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games," Econometrica, Econometric Society, vol. 88(2), pages 693-726, March.
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    24. Atsushi Kajii & Stephen Morris, 2020. "Correction to: Refinements and higher-order beliefs: a unified survey," The Japanese Economic Review, Springer, vol. 71(2), pages 351-351, April.
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    26. Stephen Morris & Daisuke Oyama & Satoru Takahashi, 2024. "Implementation via Information Design in Binary‐Action Supermodular Games," Econometrica, Econometric Society, vol. 92(3), pages 775-813, May.
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