Monotone Equilibrium Design for Matching Markets with Signaling

2024-06-04

AI Summary

This paper studies optimal wage interval design in competitive matching labor markets under asymmetric information: specifically, how a policymaker should set wage floors and ceilings to maximize social welfare when workers signal ability through education. We propose a “response-interval delegation mechanism,” embedding the planner’s ex ante committed wage interval into a signaling game and—novelty—the first integration with convex efficiency frontier analysis. Theoretically, we characterize a fundamental trade-off between ripple effects induced by the floor and pooling inefficiencies caused by the ceiling, unifying the inverse relationship between matching inefficiency and signaling costs. Methodologically, we synthesize game theory, principal-agent modeling, convex analysis, and matching theory to develop a new market design paradigm that jointly incorporates minimum wages, firm-size distribution, and employer risk preferences.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study monotone equilibrium design by a planner who chooses an interval of reactions that receivers take before senders and receivers move in matching markets with signaling. Given the convex efficiency frontier over sender surplus and receiver surplus generated by the interval delegation, the optimal reaction interval crucially depends on the ripple effect of its lower bound and on the trade-off between matching inefficiency and signaling cost savings in the top pooling region generated by its upper bound. Our analysis generates cohesive market design results that integrate the literature on minimum wage, firm size distribution, and relative risk aversion.

Problem

• Determining optimal wage band for labor market matching
• Analyzing signaling equilibrium under asymmetric information
• Improving welfare outcomes through policy intervention

Innovation

• Unique competitive signaling equilibrium proven
• Optimal wage band simplifies to threshold problem
• Parametric model improves welfare outcomes