I study games in which agents must sink their investments before they can match into partnerships that generate value. I focus on competitive matching markets where there is a public price to join any match. Despite the First Welfare Theorem for competitive markets, inefficiencies can still arise that can be interpreted as coordination failures. Armen does not invest because Bengt does not invest, and vice versa. Multiple equilibria can exist, with both efficient investment and not. The standard, Nash solution concept in these games does not help in determining if they are equally robust or stable. I argue we should replace the Nash solution concept in this context with a mild, common refinement: trembling-hand perfection. The main theorem of the paper proves that in a general class of models with general heterogeneity of types, cost of investment, and matching surplus, every perfect equilibrium is efficient and coordination failures do not exist in equilibrium. That means that in the context of competitive markets, coordination failures are not robust; the possibility of small mistakes rules out coordination failures. The only robust equilibria in competitive markets are those that are efficient even when markets are incomplete.