Before revision:  Second, dynamic matching markets exhibit a form of externality that is not present in static markets: who is available to match in a given period depends not only on the arrivals into the economy, but also on who remains unmatched from previous periods . Dynamically stable matchings always exist.
After revision:  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.