Contract theory in a VUCA world

TL;DR

This paper extends principal-agent models under Knightian uncertainty by integrating a Stackelberg equilibrium with a worst-case approach, characterizing optimal contracts through advanced stochastic methods.

Contribution

It introduces a novel framework combining Stackelberg equilibrium with worst-case analysis in a principal-agent setting under Knightian uncertainty, extending previous models without restrictive assumptions.

Findings

Optimal contracts depend on output and quadratic variation.

Agent's effort is characterized via a second order BSDE.

Principal's value is a viscosity solution of an HJBI equation.

Abstract

In this paper we investigate a Principal-Agent problem with moral hazard under Knightian uncertainty. We extend the seminal framework of Holmstr\"om and Milgrom by combining a Stackelberg equilibrium with a worst-case approach. We investigate a general model in the spirit of Cvitani\'c, Possama\"i and Touzi (2018). We show that optimal contracts depend on the output and its quadratic variation, as an extension of the works of Mastrolia and Possama\"i (2016) (by dropping all the restrictive assumptions) and Sung (2015) (by considering a general class of admissible contracts). We characterize the best reaction effort of the agent through the solution to a second order BSDE and we show that the value of the problem of the Principal is the viscosity solution of an Hamilton-Jacobi-Bellman-Isaacs equation, without needing a dynamic programming principle, by using stochastic Perron's method.