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Discrete-Time Dynamic Principal-Agent Models: Contraction Mapping Theorem and Computational Treatment

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Discrete-Time Dynamic Principal-Agent Models: Contraction Mapping Theorem and Computational Treatment. / Renner, Philipp; Schmedders, Karl.
In: Quantitative Economics, Vol. 11, No. 4, 01.11.2020, p. 1215-1251.

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Renner P, Schmedders K. Discrete-Time Dynamic Principal-Agent Models: Contraction Mapping Theorem and Computational Treatment. Quantitative Economics. 2020 Nov 1;11(4):1215-1251. doi: 10.3982/QE960

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Renner, Philipp ; Schmedders, Karl. / Discrete-Time Dynamic Principal-Agent Models : Contraction Mapping Theorem and Computational Treatment. In: Quantitative Economics. 2020 ; Vol. 11, No. 4. pp. 1215-1251.

Bibtex

@article{8298e42374ea4d32bbc44a952f86b773,
title = "Discrete-Time Dynamic Principal-Agent Models: Contraction Mapping Theorem and Computational Treatment",
abstract = "We consider discrete-time dynamic principal--agent problems with continuous choice sets and potentially multiple agents. We prove the existence of a unique solution for the principal's value function only assuming continuity of the functions and compactness of the choice sets. We do this by a contraction mapping theorem and so we also obtain a convergence result for the value function iteration. To numerically compute a solution for the problem, we have to solve a collection of static principal--agent problems at each iteration. As a result, in the discrete-time setting solving the static problem is the difficult step. If the agent's expected utility is a rational function of his action, then we can transform the bi-level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal--agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature.",
author = "Philipp Renner and Karl Schmedders",
year = "2020",
month = nov,
day = "1",
doi = "10.3982/QE960",
language = "English",
volume = "11",
pages = "1215--1251",
journal = "Quantitative Economics",
issn = "1759-7323",
publisher = "The Economic Society",
number = "4",

}

RIS

TY - JOUR

T1 - Discrete-Time Dynamic Principal-Agent Models

T2 - Contraction Mapping Theorem and Computational Treatment

AU - Renner, Philipp

AU - Schmedders, Karl

PY - 2020/11/1

Y1 - 2020/11/1

N2 - We consider discrete-time dynamic principal--agent problems with continuous choice sets and potentially multiple agents. We prove the existence of a unique solution for the principal's value function only assuming continuity of the functions and compactness of the choice sets. We do this by a contraction mapping theorem and so we also obtain a convergence result for the value function iteration. To numerically compute a solution for the problem, we have to solve a collection of static principal--agent problems at each iteration. As a result, in the discrete-time setting solving the static problem is the difficult step. If the agent's expected utility is a rational function of his action, then we can transform the bi-level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal--agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature.

AB - We consider discrete-time dynamic principal--agent problems with continuous choice sets and potentially multiple agents. We prove the existence of a unique solution for the principal's value function only assuming continuity of the functions and compactness of the choice sets. We do this by a contraction mapping theorem and so we also obtain a convergence result for the value function iteration. To numerically compute a solution for the problem, we have to solve a collection of static principal--agent problems at each iteration. As a result, in the discrete-time setting solving the static problem is the difficult step. If the agent's expected utility is a rational function of his action, then we can transform the bi-level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal--agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature.

U2 - 10.3982/QE960

DO - 10.3982/QE960

M3 - Journal article

VL - 11

SP - 1215

EP - 1251

JO - Quantitative Economics

JF - Quantitative Economics

SN - 1759-7323

IS - 4

ER -