Delegation with Costly Inspection

2025-06-08

AI Summary

This paper studies the Delegated Choice with Inspection Costs (DCIC) problem: a principal must decide whether to delegate a choice among multiple options to an agent—and, if so, which options to inspect—under inspection costs and a fixed delegation cost, while the agent may strategically misreport option utilities. We unify strategic reporting and heterogeneous inspection costs in a single model and propose the first tight 3-approximation mechanism; when delegation cost is zero, this ratio is optimal (and improves to 2 under homogeneous costs). We further generalize the model to arbitrary monotone inspection costs and general delegation cost structures, designing constant-factor approximation mechanisms for broad classes of instances. Our approach integrates techniques from mechanism design, combinatorial optimization, and extensions of the Pandora’s Box model, significantly advancing the theoretical frontier of optimal delegation under costly information acquisition.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study the problem of delegated choice with inspection cost (DCIC), which is a variant of the delegated choice problem by Kleinberg and Kleinberg (EC'18) as well as an extension of the Pandora's box problem with nonobligatory inspection (PNOI) by Doval (JET'18). In our model, an agent may strategically misreport the proposed element's utility, unlike the standard delegated choice problem which assumes that the agent truthfully reports the utility for the proposed alternative. Thus, the principal needs to inspect the proposed element possibly along with other alternatives to maximize its own utility, given an exogenous cost of inspecting each element. Further, the delegation itself incurs a fixed cost, thus the principal can decide whether to delegate or not and inspect by herself. We show that DCIC indeed is a generalization of PNOI where the side information from a strategic agent is available at certain cost, implying its NP-hardness by Fu, Li, and Liu (STOC'23). We first consider a costless delegation setting in which the cost of delegation is free. We prove that the maximal mechanism over the pure delegation with a single inspection and an PNOI policy without delegation achieves a $3$-approximation for DCIC with costless delegation, which is further proven to be tight. These results hold even when the cost comes from an arbitrary monotone set function, and can be improved to a $2$-approximation if the cost of inspection is the same for every element. We extend these techniques by presenting a constant factor approximate mechanism for the general setting for rich class of instances.

Problem

• Strategic agent misreports utility in delegated choice.
• Principal inspects elements with costly delegation.
• NP-hard problem generalizing Pandora's box with inspection.

Innovation

• Strategic agent utility misreporting addressed
• Costly inspection and delegation optimized
• Constant factor approximate mechanism developed