Multiple Referrals and Multidimensional Cheap Talk

Abstract

Cheap talk games have been widely used to analyze situations in which a policy maker needs expert advice. In previous work, agent uncertainty has almost always been modeled using a single-dimensional state variable. In this paper we prove that the dimensionality of the uncertain variable has an important qualitative impact on results and yields interesting insights into the \\mechanics " of information transmission. Contrary to the unidimensional case, with more than one dimension full transmission of information in all states of nature is typically possible, provided a very simple and intuitive condition is satis¯ed. What really matters in transmission of information is the local behavior senders ' indi®erence curves at the ideal point of the policy maker (receiver), not the proximity of players ' ideal point. This may explain the apparent con°ict between informational theories of committees and the empirical evidence on the poor alignment of preferences between the Floor and committees in legislative organizations.