Dynamic Principal-Agent Models

32 Pages Posted: 14 Apr 2016 Last revised: 23 Feb 2018

See all articles by Philipp Renner

Philipp Renner

Lancaster University

Karl Schmedders

University of Zurich

Date Written: November 14, 2016

Abstract

This paper contributes to the theoretical and numerical analysis of discrete time dynamic principal{agent problems with continuous choice sets by combining techniques from dynamic programming, bi-level optimization, real algebraic geometry, and nonlinear programming. We prove the existence of a unique solution for the principal's value function solving the recursive formulation of the principal{agent problem. By showing that the Bellman operator is a contraction mapping, we also obtain a convergence result for the value function iteration. To compute a solution for the problem we have to solve a collection of static principal{agent problems at each iteration. Under the assumption that the agent's expected utility is a rational function of his action, we can transform the bi-level optimization problem into a standard nonlinear program (NLP). The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal-agent model.

Keywords: Optimal unemployment tax, principal-agent model, repeated moral hazard

JEL Classification: C63, D80, D82

Suggested Citation

Renner, Philipp Johannes and Schmedders, Karl, Dynamic Principal-Agent Models (November 14, 2016). Swiss Finance Institute Research Paper No. 16-26. Available at SSRN: https://ssrn.com/abstract=2764140 or http://dx.doi.org/10.2139/ssrn.2764140

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
Switzerland
+41 (0)44 634 3770 (Phone)

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