Optimal Information Hierarchies

The way in which information is organized within a group matters for how the transmission of that information can be implemented. With this in mind, we introduce the concept of information hierarchies as organizational forms of distributed knowledge: In an information hierarchy, agents are partitioned into groups such that all members of a group are equally informed, and more informed (in a strong sense) than all members of lower groups. Information hierarchies can be implemented by either select public meetings or by delegated information transmission. We show that, in a general class of problems involving network interactions with complementarities, there always exists an information hierarchy among the optimal information schemes. Therefore, although the environment might display no hierarchical structuring of agents (their influences and dependencies on the state and each other might be only partially ordered), optimal design treats them hierarchically with totally ordered information. Remarkably, information hierarchies are optimal in standard design (where the best equilibrium is selected) as well as in robust design (where the worst equilibrium is selected).

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