Multi-tier hierarchies : a moral hazard approach

We consider an organization with two projects which have productive spillovers. Three agents are active in this organization: two agents, each specialized in one project, and the CEO, who is a generalist. The organization owner first allocates authority over each project to these three individuals. When an individual has authority over one project, which is not necessarily the one he is specialized in, he decides between prioritizing this project or the spillover it generates on the other project. Next, every individual decides which level of effort to exert; each agent chooses the effort in the project he specializes in, and the CEO chooses the effort impacting both projects. Each individual receives a share of the project's profits he puts effort in and a share of the project's profit for which he has authority. This creates a double moral hazard problem as none of these two decisions are contractible. Under two conditions, we show the optimality of hierarchical delegation, that is, an internal organization in which the CEO has authority over one project and one agent has authority over the project he is not specialized in. The first condition is that the CEO is more productive in exerting effort than the agents. The second condition is that prioritizing spillovers is moderately more profitable than prioritizing the profits in the project on which one has authority. We illustrate the emergence of hierarchical delegation by studying the significant reorganization that took place at Facebook in 2018.