Two-dimensional cheap talk: Necessary and sufficient conditions for perfect revelation in one dimension

Abstract

This paper develops a model of cheap talk à la Crawford and Sobel whose state variable takes values within the unit square. No characterization of all equilibria has been found. This paper focuses on equilibria where the Sender reveals all the information in the direction that is perpendicular to the vector of disagreement. The foremost result of this analysis states that there exists perfect revelation in this dimension if and only if the random state vector has components that are independent in the directions of agreement and disagreement.