Bargaining over information structures

How transparent are informational institutions if their founders have to agree on the design? We analyze a model where several agents bargain over persuasion of a single receiver. We characterize the existence of anagreement that is beneficial for all agents relative to some fixed benchmark information structure, when the preferences of agents are state-independent, and provide sufficient conditions for general preferences. We further show that a beneficial agreement exists if, for every coalition of a fixed size, there is a belief that generates enough surplus for its members. Next, we concentrate on agent-partitional environments, where for each agent there is a state where the informed decision of the receiver benefits her the most. In these environments, we define endorsement rules that fully reveal all such agent-states. Endorsement rules are Pareto efficient when providing information at all agent-states generates enough surplus, and they correspond to a Nash Bargaining solution when the environment is also symmetric. We provide two political economic applications of our model. In a running example, we discuss the implication of our model to bargaining of authoritarian elites over media policy. The last section applies the model to an electoral campaign in a multiparty democracy.