Strategy-proof and Efficient Job Matching with Participation Constraints

2026-05-03

AI Summary

This study addresses the design of many-to-one matching mechanisms in labor markets, where firms can hire multiple workers but each worker can be employed by only one firm, and workers’ valuations for firms are private information. Under the requirement of worker individual rationality, the authors employ mechanism design theory, game theory, and combinatorial optimization to establish that the Vickrey–Clarke–Groves (VCG) mechanism satisfies firm-side individual rationality if and only if firms’ preferences exhibit weak substitutability. The paper further introduces the novel concept of “strong individual rationality” and proves that it holds if and only if firms’ valuation functions are submodular. These results delineate the precise economic conditions under which the VCG mechanism is viable in employment matching, thereby laying a theoretical foundation for designing efficient, incentive-compatible mechanisms that respect participation constraints.

Abstract

We study the design of strategy-proof and efficient mechanisms satisfying participation constraints in the job-matching problem. Each firm can hire multiple workers and each worker can be employed at only one firm. While firm utilities over subsets of workers are common knowledge, worker disutilities for working at each firm are private information. The VCG mechanism is the unique mechanism that is strategy-proof, efficient, and individually rational for workers; however, it may not be individual rational for firms. We show that the VCG mechanism is individually rational for firms if and only if firm utilities satisfy a condition called weak substitutes. We then strengthen participation constraints of firms to {\sl strong individual rationality}, which requires that each firm has no incentive to fire some of the workers assigned to it. The VCG mechanism is strongly individual rational if and only if firm utilities satisfy submodularity.

Problem

• strategy-proof
• efficient
• job matching
• participation constraints
• individual rationality

Innovation

• strategy-proofness
• VCG mechanism
• weak substitutes
• submodularity
• strong individual rationality