A Polynomial Optimization Approach to Principal-Agent Problems∗

This paper presents a new method for the analysis of moral hazard principal-agent problems. The new approach avoids the stringent assumptions on the dis-tribution of outcomes made by the classical first-order approach and instead only requires the agent’s expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent’s utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn trans-forms the principal’s utility maximization problem into a nonlinear program. Under the additional assumptions that the principal’s expected utility is a polynomial and the agent’s expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows that the polynomial optimiza-tion approach, unlike the classical approach, extends to principal-agent models with multi-dimensional action sets