Agents make non-contractible investments before bargaining over who matches with whom and their terms of trade. When an agent is a price taker---in the sense that her individual investments do not change the others' payoffs---she has incentives to make socially-optimal investments.  In the context of a general non-cooperative bargaining model of coalition formation featuring dynamic entry, we show that everyone necessarily becomes a price taker as bargaining frictions vanish if and only if there is always a minimal amount of competition present in the market. On the one hand, the necessity of this condition highlights that dynamic entry need not create enough competition to guarantee price taking even if agents are arbitrarily patient. On the other hand, the sufficiency of this condition highlights that agents can be price takers even in markets that appear extremely thin at every point in time.