Contracting with discretionary bonuses

2025-11-28

AI Summary

This paper investigates the optimal dynamic compensation design for a principal hiring a risk-averse agent over a finite horizon. It formulates a continuous-time principal–agent model where incentive provision is modeled as a mixed stochastic control and optimal stopping game. Methodologically, the analysis integrates continuous-time contract theory, stochastic optimal control, and numerical simulation. The key contribution is the identification of an endogenous timing mechanism for payments—particularly sign-on bonuses—that enables *front-loaded* incentives, thereby departing from conventional *ex-post* reward paradigms. Furthermore, the study reveals significant nonlinear effects of the principal–agent disparity in patience (i.e., discount rates) and the number of bonus opportunities on both the principal’s value and the structure of optimal incentives. These findings provide novel theoretical foundations and actionable insights for designing dynamic contracts in practice.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems

Abstract

We study a continuous time contracting model in which a principal hires a risk averse agent to manage a project over a finite horizon and provides sequential payments whose timing is endogenously determined. The resulting nonzero-sum interaction between the principal and the agent is reformulated as a mixed control and stopping problem. Using numerical simulations, we investigate how factors such as the relative impatience of the parties and the number of bonus payments influence the principal's value and the structure of the optimal bonus payment scheme. A notable finding is that, in some contractual environments, the principal optimally offers a sign-on bonus to front-load incentives.

Problem

• Modeling principal-agent contracts with endogenous bonus payment timing
• Analyzing optimal bonus schemes through mixed control-stopping problems
• Investigating how impatience and payment frequency affect contract design

Innovation

• Continuous time contracting model with sequential payments
• Reformulated as mixed control and stopping problem
• Numerical simulations analyze optimal bonus payment schemes