Stability in sequential matching with incomplete information

I study a two-period matching model where one side of the market (e.g. workers) have an option to invest and delay matching in the first period. Investment increases each agent's matching surplus in the second period, by a magnitude of the worker's investment ability in the match pair. Assuming each worker's investment ability is her private information that unfolds in the second period, I define a notion of sequential stability, and show that the set of sequentially stable outcomes is a superset of the complete information stable outcomes. Moreover, with transferable utility, as long as the cost of delay coincides on the same side of the market, efficient investment occurs in any sequentially stable outcome. When every agent shares the same cost of delay, efficient investment also occurs in any sequentially stable outcome with non-transferable utility. My analysis suggests that efficient investment is a robust prediction in sequential matching markets.