DP4393 Multidimensional Cheap Talk
In this Paper we extend the cheap talk model of Crawford and Sobel (1982) to a multidimensional state space and policy space. We provide a characterization of equilibria. We focus on the question of feasibility of information transmission, for large degrees of conflict of interests between the sender and the receiver. We show that it is possible to construct equilibria with information transmission even for unboundedly large conflicts, but that any such equilibrium is based on knife-edge assumptions. We prove that influential equilibria are non-generic when the conflict between the sender and the receiver is large enough. Thus, adding more dimensions cannot improve upon information revelation when interests are too divergent.