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The speed of sequential asymptotic learning

Author

Listed:
  • Wade Hann-Caruthers
  • Vadim V. Martynov
  • Omer Tamuz
Abstract
In the classical herding literature, agents receive a private signal regarding a binary state of nature, and sequentially choose an action, after observing the actions of their predecessors. When the informativeness of private signals is unbounded, it is known that agents converge to the correct action and correct belief. We study how quickly convergence occurs, and show that it happens more slowly than it does when agents observe signals. However, we also show that the speed of learning from actions can be arbitrarily close to the speed of learning from signals. In particular, the expected time until the agents stop taking the wrong action can be either finite or infinite, depending on the private signal distribution. In the canonical case of Gaussian private signals we calculate the speed of convergence precisely, and show explicitly that, in this case, learning from actions is significantly slower than learning from signals.

Suggested Citation

  • Wade Hann-Caruthers & Vadim V. Martynov & Omer Tamuz, 2017. "The speed of sequential asymptotic learning," Papers 1707.02689, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1707.02689
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    References listed on IDEAS

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    Cited by:

    1. Yuval Peres & Miklos Z. Racz & Allan Sly & Izabella Stuhl, 2017. "How fragile are information cascades?," Papers 1711.04024, arXiv.org, revised Feb 2018.
    2. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Belief Convergence under Misspecified Learning: A Martingale Approach," Cowles Foundation Discussion Papers 2235R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2021.
    3. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Learning Efficiency of Multi-Agent Information Structures," Cowles Foundation Discussion Papers 2299R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    4. Sushil Bikhchandani & David Hirshleifer & Omer Tamuz & Ivo Welch, 2024. "Information Cascades and Social Learning," Journal of Economic Literature, American Economic Association, vol. 62(3), pages 1040-1093, September.
    5. Xuanye Wang, 2021. "Fragility of Confounded Learning," Papers 2106.07712, arXiv.org.
    6. Daron Acemoglu & Ali Makhdoumi & Azarakhsh Malekian & Asuman Ozdaglar, 2017. "Fast and Slow Learning From Reviews," NBER Working Papers 24046, National Bureau of Economic Research, Inc.
    7. Wanying Huang & Philipp Strack & Omer Tamuz, 2024. "Learning in Repeated Interactions on Networks," Econometrica, Econometric Society, vol. 92(1), pages 1-27, January.
    8. Ilai Bistritz & Nasimeh Heydaribeni & Achilleas Anastasopoulos, 2019. "Do Informational Cascades Happen with Non-myopic Agents?," Papers 1905.01327, arXiv.org, revised Jul 2022.
    9. Annie Liang & Xiaosheng Mu, 2018. "Overabundant Information and Learning Traps," PIER Working Paper Archive 18-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 27 Mar 2018.
    10. Itai Arieli & Moran Koren & Rann Smorodinsky, 2019. "The Implications of Pricing on Social Learning," Papers 1905.03452, arXiv.org.
    11. Arieli, Itai & Babichenko, Yakov & Smorodinsky, Rann, 2020. "Identifiable information structures," Games and Economic Behavior, Elsevier, vol. 120(C), pages 16-27.

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    More about this item

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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