Observational learning under imperfect information

The analysis explores Bayes-rational sequential decision making in a game with pure information externalities, where each decision maker observes only her predecessor’s binary action. Under perfect information the martingale property of the stochastic learning process is used to establish convergence of beliefs and actions. Under imperfect information, in contrast, beliefs and actions cycle forever. However, despite the instability, over time the private information is ignored and decision makers become increasingly likely to imitate their predecessors. Consequently, we observe longer and longer periods of uniform behavior, punctuated by increasingly rare switches. These results suggest that imperfect information premise provides a better theoretical description of fads and fashions. (JEL D82, D83). ∗We are grateful to Douglas Gale for his guidance, to an Associate Editor and an anonymous referee for their comments and to William J. Baumol who read carefully through the manuscript, and made invaluable suggestions on exposition. We also acknowledge helpful discussions of Jean-Pierre Benoît, Alberto Bisin, Colin F. Camerer, Andrew Caplin, Amil Dasgupta, Eric S. Maskin, Roger B. Myerson, Benjamin Polak, Matthew Rabin, Debraj Ray, Andrew Schotter, Peter Sørensen, S. R. Srinivasa Varadhan and the participants of seminars at Cornell University, CREED, Harvard University, New York University, University of Cologne, Yale University and 2001 South-East Economic Theory & International Economics Conference. †Department of Economics, New York University, 269 Mercer St., 7th Floor, New York, NY, 10003 (e-mail: [email protected], url: http://home.nyu.edu/~bc319). ‡Department of Economics, New York University, 269 Mercer St., 7th Floor, New York, NY, 10003 (e-mail: [email protected], url: http://home.nyu.edu/~sk510).