Repeated Matching Games: An Empirical Framework

2025-10-03

AI Summary

This paper addresses equilibrium modeling and structural estimation in dynamic matching markets with transferable utility and evolving individual states. It tackles three key challenges: forward-looking agents, time-varying market-clearing prices, and unobserved heterogeneity in matches. The authors extend the Shapley–Shubik framework by developing a dynamic matching model featuring both time-varying distributional equilibria and steady-state equilibria, integrating explicit market-clearing mechanisms and structural estimation with measurement error. They propose two computationally tractable and globally identified estimation algorithms. Applying the model to Swedish engineer data for the first time, they precisely identify the dynamic accumulation of job-specific human capital. Empirical results confirm the model’s feasibility, identification power, and economic interpretability. This work establishes a novel paradigm for structural analysis of dynamic matching markets.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We introduce a model of dynamic matching with transferable utility, extending the static model of Shapley and Shubik (1971). Forward-looking agents have individual states that evolve with current matches. Each period, a matching market with market-clearing prices takes place. We prove the existence of an equilibrium with time-varying distributions of agent types and show it is the solution to a social planner's problem. We also prove that a stationary equilibrium exists. We introduce econometric shocks to account for unobserved heterogeneity in match formation. We propose two algorithms to compute a stationary equilibrium. We adapt both algorithms for estimation. We estimate a model of accumulation of job-specific human capital using data on Swedish engineers.

Problem

• Modeling dynamic matching with transferable utility and evolving agent states
• Proving existence of equilibrium with time-varying agent type distributions
• Estimating job-specific human capital accumulation using Swedish engineer data

Innovation

• Dynamic matching model with transferable utility
• Algorithms compute stationary equilibrium efficiently
• Econometric shocks address unobserved heterogeneity