Randomization in dynamic principal-agent problems

Holger M. Müller

No 97-37, Papers from Sonderforschungsbreich 504

Abstract: In a seminal paper, Holmström and Milgrom (1987) examine a principal-agent problem in which an agent controls the drift of a Brownian motion. Given that the agent can revise his control continuously, they show that the optimal sharing rule is linear in aggregated output. In this paper, we examine the case where control revisions take place in arbitrarily small discrete time intervals. We show that the first-best outcome can be approached arbitrarily closely by a random spot check in conjunction with a step function. The central message of this paper is therefore that in agency problems of the sort studied by Holmström and Milgrom, linear sharing rules may not always be optimal. Random spot checks are widely used in practice and play an important role in the area of quality control.

Date: 1997
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