TY - JOUR

T1 - A Polynomial Optimization Approach to Principal-Agent Problems

AU - Renner, Philipp

AU - Schmedders, Karl

PY - 2015/3

Y1 - 2015/3

N2 - This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution 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 transforms 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 how to first approximate expected utility functions that are notrational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.

AB - This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution 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 transforms 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 how to first approximate expected utility functions that are notrational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.

U2 - 10.3982/ECTA11351

DO - 10.3982/ECTA11351

M3 - Journal article

VL - 83

SP - 729

EP - 769

JO - Econometrica

JF - Econometrica

SN - 0012-9682

IS - 2

ER -