Bargaining Foundations for Price Taking in Matching Markets

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 investments do not change her potential partners’ payoffs—she has incentives to make socially-optimal investments. Across a variety of non-cooperative bargaining models featuring dynamic entry, we show that everyone necessarily becomes a price taker as bargaining frictions vanish if and only if there is a minimal amount of competition always present in the market. The necessity of this condition highlights that dynamic entry need not create enough competition to guarantee price taking even if agents are arbitrarily patient. The sufficiency of this condition highlights that everyone can be a price taker even in markets that appear extremely thin at every point in time.