Contracts with Inspections

2024-02-26

arXiv.org

AI Summary

This paper challenges the classical “fully hidden actions” assumption in principal-agent models by studying contract design when the principal can pay to inspect a subset of the agent’s actions—enabling payment refusal upon detected violation. The core trade-off lies between positive incentives (payment structure) and negative incentives (inspection effort). We formally model both deterministic and stochastic action inspections and introduce a subset-dependent inspection cost function. Under monotone and submodular cost structures, we provide a polynomial-time algorithm for computing the optimal incentive-compatible contract; under XOS costs, we prove the problem is NP-hard. Our results unify the characterization of how inspection cost structures affect incentive-compatible contract design, establishing a novel theoretical framework and computational foundation for contract theory with partially observable actions.

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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In the classical principal-agent hidden-action model, a principal delegates the execution of a costly task to an agent for which he can choose among actions with different costs and different success probabilities to accomplish the task. To incentivize the agent to exert effort, the principal can commit to a contract, which is the amount of payment based on the task's success. A crucial assumption of this model is that the principal can only base the payment on the outcome but not on the agent's chosen action. In this work, we relax the hidden-action assumption and introduce a new model where the principal is allowed to inspect subsets of actions at some cost that depends on the inspected subset. If the principal discovers that the agent did not select the agreed-upon action through the inspection, the principal can withhold payment. This relaxation of the model introduces a broader strategy space for the principal, who now faces a tradeoff between positive incentives (increasing payment) and negative incentives (increasing inspection). We show how to find the best deterministic incentive-compatible inspection scheme for all monotone inspection cost functions. We then turn to randomized inspection schemes and show that one can efficiently find the best randomized incentive-compatible inspection scheme when the inspection cost function is submodular. We complement this result by showing that it is impossible to efficiently find the optimal randomized inspection scheme for the more general case of XOS inspection cost functions.

Problem

• Extends contract design beyond hidden-action assumptions with inspection capabilities
• Explores trade-offs between positive incentives and costly inspections in principal-agent models
• Develops algorithms for optimal inspection schemes under various cost functions

Innovation

• Introduces inspection of agent actions at cost
• Algorithms for deterministic and randomized inspection schemes
• Tractable for submodular, hard for XOS inspection costs