Observational learning under imperfect information

Abstract

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

Distinguishing Informational Cascades from Herd Behavior in the Laboratory

“…In contrast, Anderson and Holt (1997) report that about half of the herds turned out to be on the incorrect action. Theoretically, however, the difference between the probabilities of an incorrect herd in this setup and in Anderson and Holt (1997) is negligible 10 .…”

“…For example, in round 2/13 (see Table 2), the second subject favored action A even though the action she observed 10 In Anderson and Holt (1997)'s setup with signal precision 2/3, simple calculations yield that the probabilities of a correct herd, or an incorrect herd, are 70.6 percent and 28.3 percent respectively. In this setup, it cannot be found analytically since, conditional on the true state of the world, private signals are negatively correlated.…”

Aggregate information cascades

“…We denote the total number of agents who have invested before agent i by T i : agent i is informed about T i = i−1 j=1 I j . 5 In addition to observing T i , each agent i receives a symmetric binary signal σ i distributed as follows:…”

“…In an aggregate up cascade (AUC) there is a critical value T U P such that if T k = T U P all agents from k onwards choose to invest regardless of their signals. Consequently, there is some k such that T k+j = T k + j for all j = 1, ..., n − k. 5 As we have already mentioned, and will write formally below, an agent does not know his index i. The only thing agent i, the ith agent in the sequence, knows about his position is that he is not among the first Ti agents.…”

The focusing and informational effects of norms on pro-social behavior

“…8 See also Banerjee (1992), Bernheim (1994), Knez and Camerer (1995), Cason and Mui (1998), and Celen and Kariv (2004). 9 Of course, seeing what others do will likely also act as a cue that draws attention to the social norm, as in our focusing treatments.…”