Empirical Distributions of beliefs under imperfect monitoring

O. Gossner, T. TOMALA

Mathematics of Operations Research

February 2006, vol. 31, n°1, pp.13-31

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

Keywords: Stochastic process, Signals, Entropy, Repeated games

Let (xn)n be a process with values in a finite set X and law P, and let yn = f(xn) be a function of the process. At stage n, the conditional distribution pn = P(xn | x1,…,xn-1), element of ¿ = ¿(X), is the belief that a perfect observer, who observes the process online, holds on its realization at stage n. A statistician observing the signals y1,…,yn holds a belief en = P(pn | x1,…,xn) ¿ ¿(¿) on the possible predictions of the perfect observer. Given X and f, we characterize the set of limits of expected empirical distributions of the process (en) when P ranges over all possible laws of (xn)n