Incomplete-information models of large economies with anonymity: Existence and uniqueness of common priors

The paper provides a speci…cation of belief systems for models of large economies with anonymity in which aggregate states depend only on crosssection distributions of types. For belief systems satisfying certain conditions of mutual absolute continuity, the paper gives a necessary and su¢ cient condition for the existence of a common prior. Under the given conditions, the common prior is unique. Key Words : Belief systems, consistency, common prior, large economy. JEL: C70, D82, D83. 1 Incomplete Information in a Large Economy with Anonymity In this paper, I consider the existence and uniqueness of common priors in largeeconomy models with incomplete information. A large economy is represented by an atomless measure space of agents, (A;A; ): Incomplete information is modelled by means of an abstract type space [(T; T ); t; ; ]; where T; the space of potential "types", is a complete separable metrice space, T is the Borel algebra on T , t : A! T is a measurable mapping that assigns types to agents, : T ! is a measurable mapping that speci…es an agent’s payo¤ parameters or, more generally, his economic characteristics as a function of his type, and : T !M(M(T )) is a measurable mapping that speci…es an agent’s beliefs as a function of his type. For any t; the belief (t) is a probability distribution over cross-section distributions of types in the economy. Thus, (t) 2M(M(T )): For very helpful discussions and comments, I am grateful to Felix Bierbrauer, Christoph Engel, Alia Gizatulina, and Christian Hellwig.