Strategy-proof and Efficient Job Matching with Participation Constraints

TL;DR

This paper investigates the design of strategy-proof, efficient job-matching mechanisms that satisfy participation constraints, focusing on conditions for the VCG mechanism to be individually rational for firms.

Contribution

It characterizes when the VCG mechanism is individually rational for firms and introduces strong participation constraints requiring no incentive for firms to fire workers.

Findings

VCG is individually rational for firms if and only if firm utilities satisfy weak substitutes.

VCG is strongly individually rational if and only if firm utilities are submodular.

The paper establishes conditions for strategy-proof, efficient matching mechanisms under 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.