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Higher-Order Misspecification and Equilibrium Stability

Author

Listed:
  • Takeshi Murooka

    (Osaka School of International Public Policy, Osaka University)

  • Yuichi Yamamoto

    (Institute of Economic Research, Hitotsubashi University)

Abstract

This paper considers a Bayesian learning problem where strategic players jointly learn an unknown economic state, and show that one's higher-order misspecification (i.e., one's misspecification about the opponent's misspecification) can have a significant impact on the equilibrium outcome. We consider a simple environmental problem where players' production, as well as an unknown state, affects the quality of the environment. Crucially, we assume that one of the players is unrealistically optimistic about the quality of the environment. When this optimism is common knowledge, the equilibrium outcome is continuous in the amount of optimism, and hence small optimism leads to approximately correct learning of the state. In contrast, when the optimism is not common knowledge and each player is unaware of the opponent having a different view about the world, the equilibrium outcome is discontinuous, and even vanishingly small optimism leads to completely incorrect learning. We then analyze a general Bayesian learning model and discuss when such discontinuity arises.

Suggested Citation

  • Takeshi Murooka & Yuichi Yamamoto, 2023. "Higher-Order Misspecification and Equilibrium Stability," OSIPP Discussion Paper 23E002Rev., Osaka School of International Public Policy, Osaka University, revised Sep 2023.
  • Handle: RePEc:osp:wpaper:23e002rev.
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    File URL: http://www.osipp.osaka-u.ac.jp/archives/DP/2023/DP2023E002Rev.pdf
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    References listed on IDEAS

    as
    1. Perkins, S. & Leslie, D.S., 2014. "Stochastic fictitious play with continuous action sets," Journal of Economic Theory, Elsevier, vol. 152(C), pages 179-213.
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    More about this item

    Keywords

    model misspecification; learning; unawareness; convergence; stability; inferential naivety; overconfidence;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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