How Fast do Rational Agents Learn?

Abstract

A simple dynamic model of rational learning through market interaction by asymmetrically informed risk-neutral agents, uncertain about a valuation parameter but whose pooled information reveals it, is presented. The model is a variation of the classical partial equilibrium model of learning in rational expectations in which the market price is informative about the unknown parameter only through the actions of agents. It is found that learning from market prices and convergence to the rational expectations equilibrium is slow, at the rate 1/J;;l73 (where n is the number periods of market interaction), whenever the average precision of private information in the market is finite. Convergence obtains at the standard rate IjJ1i if there is a positive mass of perfectly informed agents. Comparative static results on more refined measures of the speed of convergence with respect to basic technological and informational parameters are also provided.

Media Frenzies in Markets for Financial Information

“…It avoids the criticism levied against the herding models that their discrete choice space is needed (Lee 1993, Vives 1993) and that market clearing prices interfere with the effect (Avery and Zemsky, 1998). This bubble-like outcome does not rely on agents who are not subject to transversality conditions (as in Blanchard and Watson, 1982), or are otherwise not fully rational.…”

Inertia in social learning from a summary statistic

“…Our main aims in the paper are to show that this typically creates a bias toward old information, and to study how this bias affects the speed of learning. 1 The baseline model PA (for population average) builds on Vives [19]. A new cohort of agents arrives at each stage (1, 2, ..., n, ... and so on) and must choose an action once and for all in order to minimize a quadratic loss function.…”

“…In a similar vein, Vives [19] assumes that the full sequence of actions is observed, but that each action is observed with noise, so once again beliefs cannot be perfectly recovered from actions. He shows that the rate of learning slows to n 1 3 .…”

The Relative Contributions of Private Information Sharing and Public Information Releases to Information Aggregation

“…Grossman (1976), Townsend (1978), and Grossman and Stiglitz (1980) introduce the notion of rational-expectations equilibrium to capture the idea that prices aggregate information that is dispersed in the economy. Wilson (1977), Milgrom (1981), Vives (1993), Pesendorfer and Swinkels (1997), and Reny and Perry (2006) provide strategic foundations for the rational-expectations equilibrium concept. Another strand of literature investigates information aggregation when agents learn only through private interactions.…”

“…Vives (1993) showed that when agents learn noisy public information from others, then they learn the truth at a slow speed of t 1/3 (where t is the number of periods of market interactions). The slow convergence result is due to an informational externality.…”