Dynamic matching games: stationary equilibria under varying commitments

TL;DR

This paper explores how stable matchings in dynamic markets are influenced by varying commitment levels of firms and workers, analyzing equilibrium conditions and strategic behaviors over time.

Contribution

It extends Gale-Shapley's model to dynamic, decentralized settings with varying commitments, identifying conditions for stationary equilibria.

Findings

Stable matchings can be supported as stationary equilibria under different commitment scenarios.

Agents' decisions to switch partners depend on discount factors and strategic considerations.

Different commitment levels significantly influence the structure of equilibrium outcomes.

Abstract

This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and commitments vary. Specifically, we analyze a dynamic matching game in which firms make offers to workers in each period, considering three types of commitment: (i) no commitment from either side, (ii) firms' commitment, and (iii) workers' commitment. Our results demonstrate that stable matchings can be supported as stationary equilibria under different commitment scenarios, depending on the strategies adopted by firms and workers. Furthermore, we identify key conditions, such as discount factors, that influence agents' decisions to switch partners, thereby shaping equilibrium outcomes.