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Impact of higher-order uncertainty

Author

Listed:
  • Muhamet Yildiz
  • Jonathan Weinsten
Abstract
In some games, the impact of higher-order uncertainty is very large, implying that present economic theories may be misleading as these theories assume common knowledge of the type structure after specifying the first or the second orders of beliefs. Focusing on normal-form games in which the players' strategy spaces are compact metric spaces, we show that our key condition, called "global stability under uncertainty," implies a variety of results to the effect that the impact of higher-order uncertainty is small. Our central result states that, under global stability, the maximum change in equilibrium strategies due to changes in players' beliefs at orders higher than k is exponentially decreasing in k. Therefore, given any need for precision, we can approximate equilibrium strategies by specifying only finitely many orders of beliefs

Suggested Citation

  • Muhamet Yildiz & Jonathan Weinsten, 2004. "Impact of higher-order uncertainty," Econometric Society 2004 North American Winter Meetings 157, Econometric Society.
    • Handle: RePEc:ecm:nawm04:157
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    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in Direct Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 4, pages 153-194, World Scientific Publishing Co. Pte. Ltd..
    2. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    3. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    4. ,, 2013. "Rationalizable conjectural equilibrium: A framework for robust predictions," Theoretical Economics, Econometric Society, vol. 8(2), May.
    5. Kets, Willemien, 2011. "Robustness of equilibria in anonymous local games," Journal of Economic Theory, Elsevier, vol. 146(1), pages 300-325, January.
    6. Weinstein, Jonathan & Yildiz, Muhamet, 2011. "Sensitivity of equilibrium behavior to higher-order beliefs in nice games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 288-300, May.
    7. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 377-399, April.
    8. Morris, Stephen, 2014. "Coordination, timing and common knowledge," Research in Economics, Elsevier, vol. 68(4), pages 306-314.
    9. Davide Cianciaruso & Fabrizio Germano, 2011. "Quotient Spaces of Boundedly Rational Types," Working Papers 582, Barcelona School of Economics.
    10. Satoshi Fukuda, 2024. "On the consistency among prior, posteriors, and information sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 521-565, September.
    11. 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.
    12. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    13. Mariann Ollár & Antonio Penta, 2019. "Implementation via transfers with identical but unknown distributions," Economics Working Papers 1676, Department of Economics and Business, Universitat Pompeu Fabra.
    14. Flynn, Joel P. & Sastry, Karthik A., 2023. "Strategic mistakes," Journal of Economic Theory, Elsevier, vol. 212(C).
    15. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 377-399, April.
    16. Heumann, Tibor, 2019. "An ascending auction with multi-dimensional signals," Journal of Economic Theory, Elsevier, vol. 184(C).
    17. Qin, Cheng-Zhong & Yang, Chun-Lei, 2009. "An Explicit Approach to Modeling Finite-Order Type Spaces and Applications," University of California at Santa Barbara, Economics Working Paper Series qt8hq7j89k, Department of Economics, UC Santa Barbara.
    18. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy & Omer Tamuz, 2020. "Feasible Joint Posterior Beliefs," Papers 2002.11362, arXiv.org, revised Dec 2020.
    19. Jungsuk Han & Albert S. Kyle, 2018. "Speculative Equilibrium with Differences in Higher-Order Beliefs," Management Science, INFORMS, vol. 64(9), pages 4317-4332, September.
    20. Qin, Cheng-Zhong & Yang, Chun-Lei, 2013. "Finite-order type spaces and applications," Journal of Economic Theory, Elsevier, vol. 148(2), pages 689-719.
    21. Xiao, Tiaojun & Qi, Xiangtong, 2010. "Strategic wholesale pricing in a supply chain with a potential entrant," European Journal of Operational Research, Elsevier, vol. 202(2), pages 444-455, April.
    22. Rong, Kang, 2013. "Impact of second-order uncertainty on the efficiency of the 0.5-double auction," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 67-71.
    23. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.

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    More about this item

    Keywords

    higher-order uncertainty; robustness of equilibrium; stability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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