Abstract
Observational learning occurs when privately informed individuals sequentially choose among finitely many actions after seeing predecessors’ choices. We summarise the general theory of this paradigm: belief convergence forces action convergence; specifically, copycat ‘herds’ arise. Also, beliefs converge to a point mass on the truth exactly when the private information is not uniformly bounded. This subsumes two key findings of the original herding literature: With multinomial signals, cascades occur, where individuals rationally ignore their private signals, and incorrect herds start with positive probability. The framework is flexible – some individuals may be committed to an action, or individuals may have divergent cardinal or even ordinal preferences.
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Notes
- 1.
Still, it helps to introspect on exactly why no such contrarian can arise. Let the chance that the kth individual breaks the herd be pk, given the state. If these chances vanish fast enough that they are summable, then their tail sum can be made as small as desired. Then by conditional independence, the chance that no one among 1, 2, … , k breaks the herd is positive:
$$ \left(1-{p}_1\right)\cdots \left(1-{p}_k\right)>1-{p}_1-{p}_2-\cdots -{p}_k>0. $$
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Smith, L., Sørensen, P.N. (2018). Observational Learning. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2990
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2990
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