Anonymity, Equal Treatment, and Overconfidence: Constraints on Communication May Enhance Information Transmission

This paper offers a simple but rich framework to study communication subject to various constraints such as anonymity requirements, equal treatment of multiple agents, overconfidence of an expert, and garbling, by extending the cheap talk model of Crawford and Sobel (1982). Common to these seemingly distinct types of constraints in communication is that the action by a decision maker is less sensitive to a message than without such constraints. Reduced sensitivity can alter the structure of informative equilibria dramatically, and leads to a type of informational distortion, termed incentives to exaggerate, which differs qualitatively from the well-known incentives to overstate/understate. We demonstrate that the two different types of distortion may partly offset each other, so the introduction of the costraints may be beneficial when the level to conflict between communicating parties is large. Our model can also be applied to study communication in public good provision where equal treatment is often implicitly assumed.