The speed of sequential asymptotic learning
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.
Additional Information
© 2017 Elsevier Inc. Received 7 March 2017, Revised 27 September 2017, Accepted 21 November 2017, Available online 1 December 2017. The authors would like to thank Christophe Chamley, Gil Refael, Peter Sørensen, Philipp Strack, Ye Wang, Ivo Welch and Leeat Yariv for helpful comments and discussions. This work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz).Attached Files
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Additional details
- Eprint ID
- 78984
- Resolver ID
- CaltechAUTHORS:20170712-081145954
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2017-07-12Created from EPrint's datestamp field
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2021-11-15Created from EPrint's last_modified field