Empirical distributions of beliefs under imperfect observation

• 成果类型: Article
• 署名作者: Gossner, O; Tomala, T
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Universite PSL; Ecole Normale Superieure (ENS); Ecole des Hautes Etudes en Sciences Sociales (EHESS); Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Northwestern University; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1050.0174
• 发表日期: 2006
• 页码: 13-30
• 关键词: Repeated games; Bounded recall; COMMUNICATION

摘要

Let (x(n))(n) be a process with values in a finite set X and law P, and let y(n) = f(x(n)) be a function of the process. At stage n, the conditional distribution p(n) = P(x(n) vertical bar x(1),..., x(n-1)), element of Pi = Delta(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,..., y(n) holds a belief e(n) = P(p(n) vertical bar x(1),..., x(n)) is an element of Delta(Pi) 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 (e(n)) when P ranges over all possible laws of (x(n))(n).