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... his information set, and he acts according to the information conveyed by the actions of previous individuals. Therefore, he ignores his private information and starts a cascade. PROPOSITION 1. If assumptions 1 and 2 hold, then as the number of individuals increases, the probability that a cascade eventually starts approaches one. While we have shown that cascades must eventually occur, perhaps the more interesting point is that they will often be wrong.'6 In an 14 The monotone likelihood ratio property is a standard assumption in models in which inferences must be drawn from a noisy signal. Milgrom (1981) provides a presentation and applications. 15 It is a mild assumption. If VI, v2 . Vs and C are drawn randomly from any nonatomic probability measure, assumption 2 is satisfied with probability one. This assumption prevents asymptotic indifference but is not a tie-breaking convention. 16 proof of proposition 1 is based on the idea that many observations of informative actions would lead with high probability to nearly perfect knowledge of value. Thus with high probability a cascade must start at or before such a point, but this cascade will often be an incorrect one that started much earlier. ...

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...n for monotonicity.9 We now show, however, that, once we take into account the possibility that the agent may be indifferent between several actions at an 9See Mirrlees [11] or Holmstrom [7]. Milgrom =-=[9]-=- has shown that MLRC, as stated here, implies the differential version of the monotone likelihood condition which is to be found in Mirrlees [11] or Holmstrom [7].24 S. J. GROSSMAN AND 0. D. HART opt...

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..., if consumers are all rational (or aware), shrouding should actually hurt the bank or printer manufacturer, because rational consumers will expect the worse from a firm that shrouds [Jovanovic 1982; =-=Milgrom 1981-=-]. Any information that is hidden in the fine print—or excluded from marketing materials altogether—is not likely to be favorable to consumers. Rational consumers will infer that hidden prices are lik...

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... companies fail to state clearly which items are being excluded (see Mann, 2001b), in contrast with the full-disclosure ‘unravelling’ prediction of the earliest disclosure models (see Grossman, 1981; =-=Milgrom, 1981-=-). Incomplete disclosure may reflect costs of doing so, such as the revelation of information to competitors (see, e.g., the discussion and references in Verrecchia, 2001). However, a fuller GAAP disc...