Dynamic Principal-Agent Models

Philipp Renner and Karl Schmedders

No 16-26, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: This paper contributes to the theoretical and numerical analysis of discrete time dynamic principal-agent problems with continuous choice sets. We first provide a new and simplified proof for the recursive reformulation of the sequential dynamic principal-agent relationship. Next we prove the existence of a unique solution for the principal's value function, which solves the dynamic programming problem in the recursive formulation, by showing that the Bellman operator is a contraction mapping. Therefore, the theorem also provides 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). We can then solve these nonlinear problems with a standard NLP solver. 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.

Keywords: Optimal unemployment tax; principal-agent model; repeated moral hazard (search for similar items in EconPapers)
JEL-codes: C63 D80 D82 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2016-04
New Economics Papers: this item is included in nep-cmp, nep-cse, nep-dge, nep-mic, nep-ore and nep-upt
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1626

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