COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1552

Informational Herding and Optimal Experimentation

Lones Smith
Department of Economics, University of Michigan
and
Peter Norman Sorensen
Department of Economics, University of Copenhagen

January 2006

We show that far from capturing a formally new phenomenon, informational herding is really a special case of single-person experimentation — and 'bad herds' the typical failure of complete learning. We then analyze the analogous team equilibrium, where individuals maximize the present discounted welfare of posterity. To do so, we generalize Gittins indices to our non-bandit learning problem, and thereby characterize when contrarian behaviour arises: (i) While herds are still constrained efficient, they arise for a strictly smaller belief set. (ii) A log-concave log-likelihood ratio density robustly ensures that individuals should lean more against their myopic preference for an action the more popular it becomes.

Keywords: Bayesian learning, value function, herding, experimentation, log concavity, Gittins index, team equilibrium

JEL Classification: D83