A Polynomial Optimization Approach to Principal-Agent Problems

49 Pages Posted: 3 Dec 2012 Last revised: 15 Oct 2014

See all articles by Philipp Renner

Philipp Renner

Lancaster University

Karl Schmedders

University of Zurich

Date Written: October 14, 2014


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 not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to non-polynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal-agent models with multi-dimensional action sets.

Keywords: Principal-agent model, moral hazard, first order approach, polynomials

JEL Classification: C63, D80, D82

Suggested Citation

Renner, Philipp Johannes and Schmedders, Karl, A Polynomial Optimization Approach to Principal-Agent Problems (October 14, 2014). Econometrica, Forthcoming; Swiss Finance Institute Research Paper No. 12-35. Available at SSRN: https://ssrn.com/abstract=2179445 or http://dx.doi.org/10.2139/ssrn.2179445

Philipp Johannes Renner

Lancaster University ( email )

Managment School
Department of Economics
Lancaster LA1 4YX, Lancashire LA1 4YX
United Kingdom

Karl Schmedders (Contact Author)

University of Zurich ( email )

Moussonstrasse 15
Zürich, CH-8044
+41 (0)44 634 3770 (Phone)

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