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Uncertain Rationality, Depth of Reasoning and Robustness in Games with Incomplete Information

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Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989) Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with multiple rationalizable (ICR) actions, there exist similar types with unique rationalizable action. This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz's discontinuity. We weaken ICR to ICR-x, where x is a sequence whose n-th term is the probability players attach to (n - 1)th-order belief in rationality. We find that Weinstein and Yildiz's discontinuity holds when higher-order belief in rationality remains above some threshold (constant x), but fails when higher-order belief in rationality eventually becomes low enough (x converging to 0).

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  • Fabrizio Germano & Jonathan Weinstein & Peio Zuazo-Garin, 2016. "Uncertain Rationality, Depth of Reasoning and Robustness in Games with Incomplete Information," Economics Working Papers 1548, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1548
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    Cited by:

    1. Francesco Cerigioni & Fabrizio Germano & Pedro Rey Biel & Peio Zuazo-Garin, 2019. "Higher Orders of Rationality and the Structure of Games," Working Papers 1120, Barcelona School of Economics.
    2. repec:upd:utmpwp:006 is not listed on IDEAS
    3. Aviad Heifetz, 2019. "Robust multiplicity with (transfinitely) vanishing naiveté," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1277-1296, December.
    4. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
    5. Evan Piermont & Peio Zuazo-Garin, 2021. "Heterogeneously Perceived Incentives in Dynamic Environments: Rationalization, Robustness and Unique Selections," Papers 2105.06772, arXiv.org.
    6. 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.
    7. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2022. "Robust refinement of rationalizability with arbitrary payoff uncertainty," Games and Economic Behavior, Elsevier, vol. 136(C), pages 485-504.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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