Theoretical Economics 14 (2019), 1435–1482

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### Optimal dynamic contracting: the first-order approach and beyond

*Marco Battaglini, Rohit Lamba*

#### Abstract

We explore the conditions under which the "first-order approach" (FO-approach) can be used to characterize profit maximizing contracts in dynamic principal-agent models. The FO-approach works when the resulting FO-optimal contract satisfies a particularly strong form of monotonicity in types, a condition that is satisfied in most of the solved examples studied in the literature. The main result of our paper is to show that except for non-generic choices of the stochastic process governing the types' evolution, monotonicity and more generally incentive compatibility are necessarily violated by the FO-optimal contract if the frequency of interactions is sufficiently high (or equivalently if the discount factor, time horizon and persistence in types are sufficiently large). This suggests that the applicability of the FO-approach is problematic in environments in which expected continuation values are important relative to per-period payoffs. We present conditions under which a class of incentive compatible contracts that can be easily characterized is approximately optimal.

Keywords: Contract theory, dynamic contracts

JEL classification: D82, D86

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