Optimal contracts with a risk‐taking agent

Abstract

Consider an agent who can costlessly add mean-preserving noise to his output. To deter such risk-taking, the principal optimally offers a contract that makes the agent's utility concave in output. If the agent is risk-neutral and protected by limited liability, this concavity constraint binds and so linear contracts maximize profit. If the agent is risk averse, the concavity constraint might bind for some outputs but not others. We characterize the unique profit-maximizing contract and show how deterring risk-taking affects the insurance-incentive trade-off. Our logic extends to costly risk-taking and to dynamic settings where the agent can shift output over time.

A General Framework for Robust Contracting Models

“…In this section, we give an example to illustrate how the same methodology we have used to identify organization-free conditions for linear contracts can also be used for other kinds of contracts. This example is inspired by Barron, Georgiadis, and Swinkels (2020). They consider a Bayesian principal-agent model in which the agent can, after privately observing output, costlessly add mean-zero random noise to produce the "final" output, and only final output is contractible.…”

“…The literature on this theme has generally drawn on the idea that there may be a large space of possible actions by the agent, a notion that we formalize subsequently under the name of “Richness.” With a narrow space of possible actions, the structure of the optimal contract may be nonlinear and finely tuned to the known possibilities; but under richness, any such nonlinearities are vulnerable to strategic gaming by the agent. Incarnations of this idea have appeared in static moral hazard models (Diamond (1998), Carroll (2015), Barron, Georgiadis, and Swinkels (2020), Antić (2021)), dynamic moral hazard (Holmström and Milgrom (1987)), and screening as well (Malenko and Tsoy (2020)).…”

Dynamic Compensation Under Uncertainty Shocks and Limited Commitment

“…It follows DeMarzo and Sannikov (2006), Biais et al (2007), Sannikov (2008), andZhu (2013) in modeling productivity management. It belongs to the broad research on risk management in static settings (e.g., Diamond (1998), Biais and Casamatta (1999), Palomino and Prat (2003), Hellwig (2009), and Ray and Robson (2012)) and in dynamic settings (Makarov and Plantin (2015), Barron, Georgiadis, and Swinkels (2020)). These studies typically have a 1-dimensional agency problem: The agent either chooses effort or risk.…”

Optimal Monitoring Design

“… Other papers provide conditions under which linear contracts are optimal; see, for example, Holmström and Milgrom (), Carroll (), and Barron, Georgiadis, and Swinkels (). …”