Strategy-proof and Efficient Job Matching with Participation Constraints
Sushil Bikhchandani, Debasis Mishra
TLDR
This paper analyzes the VCG mechanism's strategy-proofness, efficiency, and individual rationality for job matching under various firm utility conditions.
Key contributions
- VCG is the unique mechanism for strategy-proof, efficient, and worker-individually rational job matching.
- Shows VCG is individually rational for firms if and only if firm utilities satisfy "weak substitutes".
- Demonstrates VCG is "strongly individual rational" for firms if and only if firm utilities are submodular.
Why it matters
This paper provides crucial insights into the applicability of the VCG mechanism in job matching markets. It precisely defines the conditions on firm utilities required for VCG to satisfy various participation constraints, which is vital for designing robust and fair matching systems.
Original 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.
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