# Dynamically Stable Matching

## TL;DR

This paper introduces the concept of dynamic stability for two-sided matching markets where matches are formed over time, ensuring stability and timely participation despite externalities and evolving agent availability.

## Contribution

It defines a new stability notion for dynamic markets, proves that such matchings always exist, and highlights their importance for timely agent participation.

## Key findings

- Dynamic stable matchings always exist.
- Dynamic stability ensures agents participate promptly.
- Externalities in dynamic markets are addressed by the new stability concept.

## Abstract

I introduce a stability notion, dynamic stability, for two-sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one-to-one, and (iii) matching is irreversible. The definition addresses two conceptual issues. First, since not all agents are available to match at the same time, one must establish which agents are allowed to form blocking pairs. Second, dynamic matching markets exhibit a form of externality that is not present in static markets: an agent's payoff from remaining unmatched cannot be defined independently of what other contemporaneous agents' outcomes are. Dynamically stable matchings always exist. Dynamic stability is a necessary condition to ensure timely participation in the economy by ensuring that agents do not strategically delay the time at which they are available to match.