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Impact of higher-order uncertainty

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  • Weinstein, Jonathan
  • Yildiz, Muhamet

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
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  • Weinstein, Jonathan & Yildiz, Muhamet, 2007. "Impact of higher-order uncertainty," Games and Economic Behavior, Elsevier, vol. 60(1), pages 200-212, July.
  • Handle: RePEc:eee:gamebe:v:60:y:2007:i:1:p:200-212
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    Cited by:

    1. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    2. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    3. Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1175-1204.
    4. 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.
    5. 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.
    6. repec:eee:macchp:v2-1065 is not listed on IDEAS
    7. Esponda, Ignacio, 2013. "Rationalizable conjectural equilibrium: A framework for robust predictions," Theoretical Economics, Econometric Society, vol. 8(2), May.
    8. 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.
    9. Morris, Stephen, 2014. "Coordination, timing and common knowledge," Research in Economics, Elsevier, vol. 68(4), pages 306-314.
    10. Davide Cianciaruso & Fabrizio Germano, 2011. "Quotient Spaces of Boundedly Rational Types," Working Papers 582, Barcelona Graduate School of Economics.
    11. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    12. Qin, Cheng-Zhong & Yang, Chun-Lei, 2013. "Finite-order type spaces and applications," Journal of Economic Theory, Elsevier, vol. 148(2), pages 689-719.
    13. 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.
    14. Kets, Willemien, 2011. "Robustness of equilibria in anonymous local games," Journal of Economic Theory, Elsevier, vol. 146(1), pages 300-325, January.
    15. 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.

    More about this item

    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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