On the Convergence of Informational Cascades

Observational Learning

“…When private signals sufficiently violate a log-concavity condition, a cascade can arise. Lee (1993) noted that beliefs can be perfectly revealed when the action space is continuous just like the belief space. The social learning paradigm instead by and large explores when a coarse action set communicates the private beliefs of decision makers.…”

Financial Crises as Herds: Overturning the Critiques

“…An equilibrium in this model is a collection of strategies x t (h it , Q Bt , Q St ), prices Q Bt (h t ) and Q St (h t ), and beliefs p t (h t ), p B (h t , Q Bt ), p S (h t , Q St ), and p t (h it ) such that (i) the strategies x t (·) are optimal for the investors, (ii) the prices set by market makers maximize profits given in (14) and (15), (iii) a market maker's profits evaluated at Q Bt (h t ) and Q St (h t ) are equal to zero, and (iv) where possible, the beliefs satisfy Bayes' rule.…”

“…Similar reasoning establishes that the posterior of the market maker to whom agents sell is given by P D (p), or (19). Given these posteriors, it follows from (14) and (15) that the expected profits of the market maker are zero at the prices given by (16) and (17).…”

“…Clearly, now a buy or sell decision does not convey any information to the market maker, and the market maker's posterior stays at the public belief p. Substituting these posteriors and the equilibrium prices into (14) and (15) gives that the expected profits of the market maker are zero at these prices. Clearly, any deviation by a market maker leads to negative profits.…”

“…The opportunity cost of selling the project to an agent is max{p S (h t , Q 0 Bt )A−1, 0}. Thus, if an agent buys a project, the profits of the market maker are given by (14). Clearly, if an agent sells a project, the profits of the market maker are given by (15).…”