# Large-scale principal-agent models

# Large-scale principal-agent models

**In-Person Talk **

In this talk, we will introduce two problems of contract theory, in continuous–time, with a multitude of agents. First, we will study a model of optimal contracting in a hierarchy, which generalises the one-period framework of Sung (2015). The hierarchy is modeled by a series of interlinked principal-agent problems, leading to a sequence of Stackelberg equilibria. More precisely, the principal (she) can contract with a manager (he), to incentivise him to act in her best interest, despite only observing the net benefits of the total hierarchy. The manager in turn subcontracts the agents below him. Both agents and the manager each independently control a stochastic process representing their outcome. We will see through a simple example that even if the agents only control the drift of their outcome, the manager controls the volatility of the Agents’ continuation utility. Even this first simple example justifies the use of recent results on optimal contracting for drift and volatility control, and therefore the theory on second-order BSDEs. Then, we will introduce the second problem, namely optimal contracting for demand-response management, which consists in extending the model by Aïd, Possamaï, and Touzi (2019) to a mean-field of consumers. Finally, we will conclude by mentioning that this large-scale principal-agent model can be used to address many other situations.