Public private partnerships contract under moral hazard and ambiguous information

Abstract

This paper studies optimal Public Private Partnerships contract between a public entity and a consortium, with the possibility for the public to stop the contract. The public (“she”) pays a continuous rent to the consortium (“he”), while the latter gives a response characterized by his effort. Usually, the public cannot observe the effort done by the consortium, in addition, the law of the Agent’s effort which affects the distribution of the total output is to be chosen over a set of probabilities, leading to a Principal-Agent problem with moral hazard and Knightian uncertainty characterized by [Formula: see text]-ignorance. Our problem is formulated as a Stackelberg leadership model between the public and the consortium. This problem is solved in three steps. The first one consists on characterizing the worst case, then we derive the Agent’s best response. In the third step, we solve the Principal problem by maximizing the social value of the project minus the rent paid, which is a standard stochastic control problem. The public value function is characterized by the solution of an associated Hamilton–Jacobi–Bellman variational inequality. The public value function, the optimal effort and the optimal rent are computed numerically in a feedback form by using the Howard algorithm. We show numerically that each increase in the degree of Knightian uncertainty leads to increase the optimal effort, and decrease the value function.