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

Author

Listed:
  • Fabrizio Germano
  • Jonathan Weinstein
  • Peio Zuazo-Garin

Abstract

Predictions under common knowledge of payoffs may differ from those under arbi- trarily, 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?, where ? is a sequence whose nth 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 ?), but fails when higher-order belief in rationality eventually becomes low enough (? converging to 0).

Suggested Citation

  • Fabrizio Germano & Jonathan Weinstein & Peio Zuazo-Garin, 2017. "Uncertain Rationality, Depth of Reasoning and Robustness in Games with Incomplete Information," Working Papers 947, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:947
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    References listed on IDEAS

    as
    1. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, March.
    2. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society, vol. 13(1), January.
    3. 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.
    4. 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.
    5. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    6. Chen, Yi-Chun & di Tillio, Alfredo & Faingold, Eduardo & Xiong, Siyang, 2010. "Uniform topologies on types," Theoretical Economics, Econometric Society, vol. 5(3), September.
    7. 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.
    8. Penta, Antonio, 2013. "On the structure of rationalizability for arbitrary spaces of uncertainty," Theoretical Economics, Econometric Society, vol. 8(2), May.
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    Cited by:

    1. 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.
    2. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    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. Francesco Cerigioni & Fabrizio Germano & Pedro Rey-Biel & Peio Zuazo-Garin, 2019. "Higher orders of rationality and the structure of games," Economics Working Papers 1672, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Evan Piermont & Peio Zuazo-Garin, 2021. "Heterogeneously Perceived Incentives in Dynamic Environments: Rationalization, Robustness and Unique Selections," Papers 2105.06772, arXiv.org.

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    More about this item

    Keywords

    robustness; Rationalizability; bounded rationality; Incomplete Information; belief hierarchies;
    All these keywords.

    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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