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Bounded Reasoning and Higher-Order Uncertainty

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  • Willemien Kets

Abstract

The standard framework for analyzing games with incomplete information models players as if they form beliefs about their opponents' beliefs about their opponents' beliefs and so on, that is, as if players have an infinite depth of reasoning. This strong assumption has nontrivial implications, as is well-known. This paper therefore generalizes the type spaces of Harsanyi (1967-1968) to model that players can have a finite depth of reasoning. The innovation is that players can have a coarse perception of the higher-order beliefs of other players, thus formalizing the small-world idea of Savage (1954) in a type-space context. Unlike the case in other models of finite-order reasoning, players with a finite depth of reasoning can have nontrivial higher-order beliefs about certain events. Intuitively, some higher-order events are generated by events of lower orders, making it possible for players to reason about them, even if they have a finite depth of reasoning.

Suggested Citation

  • Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1547
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    Citations

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    Cited by:

    1. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society.
    2. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    3. Larbi Alaoui & Antonio Penta, 2016. "Endogenous Depth of Reasoning," Review of Economic Studies, Oxford University Press, vol. 83(4), pages 1297-1333.
    4. Nicola Gennaioli & Rafael La Porta & Florencio Lopez-de-Silanes & Andrei Shleifer, 2013. "Human Capital and Regional Development," The Quarterly Journal of Economics, Oxford University Press, pages 105-164.
    5. Olga Gorelkina, 2015. "The Expected Externality Mechanism in a Level-k Environment," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_03, Max Planck Institute for Research on Collective Goods.
    6. repec:eee:matsoc:v:90:y:2017:i:c:p:191-207 is not listed on IDEAS
    7. Andrés Perea & Willemien Kets, 2016. "When Do Types Induce the Same Belief Hierarchy?," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-17, October.
    8. repec:esx:essedp:722 is not listed on IDEAS
    9. Tsakas Elias, 2012. "Rational belief hierarchies," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Willemien Kets, 2014. "Finite Depth of Reasoning and Equilibrium Play in Games with Incomplete Information," Discussion Papers 1569, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Larbi Alaoui & Antonio Penta, 2017. "Reasoning about Others’ Reasoning," Working Papers 1003, Barcelona Graduate School of Economics.
    12. Edward L. Glaeser & Giacomo A. M. Ponzetto & Andrei Shleifer, 2016. "Securing Property Rights," Working Paper 463441, Harvard University OpenScholar.
    13. Larbi Alaoui & Antonio Penta, 2017. "Reasoning about others’ reasoning," Economics Working Papers 1587, Department of Economics and Business, Universitat Pompeu Fabra.
    14. Davide Cianciaruso & Fabrizio Germano, 2011. "Quotient Spaces of Boundedly Rational Types," Discussion Papers 1539, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
    16. Davide Cianciaruso & Fabrizio Germano, 2011. "Quotient Spaces of Boundedly Rational Types," Discussion Papers 1539, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

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