Informational Herding and Optimal Experimentation

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.

[1]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[2]  Milton Sobel,et al.  An Essentially Complete Class of Decision Functions for Certain Standard Sequential Problems , 1953 .

[3]  R. Radner,et al.  Team Decision Problems , 1962 .

[4]  M. Rothschild.  A two-armed bandit theory of market pricing , 1974 .

[5]  W. Hildenbrand.  Core and Equilibria of a Large Economy. , 1974 .

[6]  K. Okuguchi.  Matrices with dominant diagonal blocks and economic theory , 1978 .

[7]  J. Gittins.  Bandit processes and dynamic allocation indices , 1979 .

[8]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[9]  Jack Schechtman,et al.  A Simple Competitive Model with Production and Storage , 1983 .

[10]  A. McLennan.  Price dispersion and incomplete learning in the long run , 1984 .

[11]  Dimitri P. Bertsekas,et al.  Dynamic Programming: Deterministic and Stochastic Models , 1987 .

[12]  N. Kiefer,et al.  Controlling a Stochastic Process with Unknown Parameters , 1988 .

[13]  Nancy L. Stokey,et al.  Recursive methods in economic dynamics , 1989 .

[14]  X. Vives.  How Fast do Rational Agents Learn , 1993 .

[15]  Narasimhan Jegadeesh,et al.  Evidence of Predictable Behavior of Security Returns , 1990 .

[16]  Rabah Amir,et al.  Sensitivity analysis of multisector optimal economic dynamics , 1991 .

[17]  B. Jullien,et al.  OPTIMAL LEARNING BY EXPERIMENTATION , 1991 .

[18]  Margaret Meyer,et al.  Learning from Coarse Information: Biased Contests and Career Profiles , 1991 .

[19]  James Dow,et al.  Search Decisions with Limited Memory , 1991 .

[20]  A. Banerjee,et al.  A Simple Model of Herd Behavior , 1992 .

[21]  S. Bikhchandani,et al.  You have printed the following article : A Theory of Fads , Fashion , Custom , and Cultural Change as Informational Cascades , 2007 .

[22]  Leonard J. Mirman,et al.  EXPERIMENTAL CONSUMPTION FOR A GENERAL CLASS OF DISTURBANCE DENSITIES , 1993 .

[23]  Douglas Gale,et al.  Information Revelation and Strategic Delay in a Model of Investment , 1994 .

[24]  Mathias Dewatripont,et al.  The Prudential Regulation of Banks , 1994 .

[25]  R. Shiller.  Conversation, Information, and Herd Behavior , 1995 .

[26]  Kenneth Burdett,et al.  Truncated means and variances , 1996 .

[27]  Lones Smith,et al.  Pathological Outcomes of Observational Learning , 2000 .

[28]  X. Vives.  Learning from others: A welfare analysis , 1997 .

[29]  Xavier Vives,et al.  Strategic Behavior and Price Discovery , 1997 .

[30]  Xavier Vives,et al.  Informational Externalities, Herding and Incentives , 2001 .

[31]  Matthew Doyle.  Informational Externalities, Strategic Delay, and the Search for Optimal Policy , 2002 .

[32]  Daniel Sgroi,et al.  Optimizing Information in the Herd: Guinea Pigs, Profits, and Welfare , 2002, Games Econ. Behav..

[33]  L. Vesterlund,et al.  Dynamic Monopoly Pricing and Herding , 2005 .

[34]  Kevin D. Cotter,et al.  Non-concave dynamic programming , 2006 .

[35]  Bruno Strulovici,et al.  Comparative Statics, Informativeness, and the Interval Dominance Order , 2009 .

[36]  David Gill,et al.  Sequential Decisions with Tests , 2008, Games Econ. Behav..