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

Renner, Philipp and Schmedders, Karl (2020) Discrete-Time Dynamic Principal--Agent Models:Contraction Mapping Theorem and Computational Treatment. Quantitative Economics. ISSN 1759-7323 (In Press)

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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.

Item Type:
Journal Article
Journal or Publication Title:
Quantitative Economics
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2000/2002
Subjects:
ID Code:
144023
Deposited By:
Deposited On:
14 May 2020 08:55
Refereed?:
Yes
Published?:
In Press
Last Modified:
21 Sep 2020 00:22