INFORMATIONAL CASCADES 999 actions convey no information about private signals;thus an individ- ual's action does not improve later decisions. Rogers and Shoemaker (1971)summarize research on the ability of outsiders(or"change agents")to bring about the adoption of desir- able innovations within communities.They offer the general proposi- tion that"change agent success is positively related to his efforts in increasing his clients'ability to evaluate innovations"(p.247).This is consistent with the prediction of this binary example that as the preci- sion of the signal,p,increases,a correct cascade starts with higher probability and,on average,earlier. It is instructive to compare the outcome in the previous-actions- observable(PAO)regime to that of the more informative previous- signals-observable(PSO)regime.In the binary signal case,PAO leads to a more uniform outcome.Following any given sequence of signal realizations,the two regimes lead to precisely identical outcomes,un- til a cascade begins in the PAO regime.However,in the PAO regime, after a cascade starts it is never reversed.In the PSO regime,even if an individual does not follow his private signal,it joins the common pool of knowledge.Hence,a long enough series of opposing signals will eventually cause people's behavior to switch.Thus the PAO leads to greater uniformity.We shall argue in Section V that this uniformity is brittle:small shocks can easily shift the behavior of many indi- viduals. B.A General Model We now show that under mild assumptions on the signals and values, cascades will always arise.Let there be a sequence of individuals i 1,2,...,n,...,each deciding whether to adopt some behavior or to reject it.Each individual observes the decisions of all those ahead of him.The order of individuals is exogenous and is known to all.All individuals have the same cost of adopting,C,and gain to adopting,V.The gain V has a finite set of possible values,v<v2 <..<vs,and the decision is not trivial (v<C<vs).The prior probability that V =v is denoted We use the concept of perfect Bayesian equilibrium.Since an indi- vidual's payoffs do not depend on what later individuals do,there is no incentive to make an out-of-equilibrium move to try to influence a later player.Thus,without loss of generality,we assume that if any player is observed to deviate from the equilibrium,either by rejecting when he should have adopted regardless of his signal realization or by adopting when he should have rejected regardless,then subsequent individuals have the same beliefs as though he had chosen his correct (equilibrium)action