Constrained Communication with Multiple Agents: Anonymity, Equal Treatment, and Public Good Provision

This paper studies information transmission subject to anonymity requirements and communication in public good provision without transfers. The structure of informative equilibria under anonymity or in public good provision can differ substantially from that of direct one-to-one communication, and in particular we distinguish i) informational distortion caused by the intrinsic divergence of preferences between the decision maker and each agent; and ii) informational distortion caused by the decision maker's weak response to each agent's message due to the equal treatment of all agents that results from anonymity or the nature of public goods. We examine the interaction between these two types of distortion and demonstrate that they may partly offset one another. Information transmission and welfare can be enhanced by introducing the second type of distortion through anonymity when the first type of distortion is severe. In public good provision where the intrinsic preference divergence between the utilitarian decision maker and each agent is absent, as the number of agents becomes larger the quality of communication diminishes and informative equilibria converge to the one that can be played by letting each agent report a binary message (e.g. "yes" or "no") even if their preferences and the decision are continuous.