We study equilibrium prices and trade volume in a market with several identical buyers and a seller who commits to an inventory and then offers goods sequentially. Prices are determined by a strategic costly bargaining process with a random sequence of proponents. A unique subgame perfect equilibrium exists, characterized by no costly delays and heterogeneous sale prices. In equilibrium constraining capacity is a bargaining tactic the seller uses to improve a weak bargaining position. With capacity constraints, sale prices approach the outcome of an auction as bargaining costs vanish. The framework provides a building block for price formation in models of equilibrium search with multilateral matching, and offers a rationale for the adoption of single-unit auctions with fixed reservation price.
Camera, G., and C. Selcuk (2010). Multi-player bargaining with endogenous capacity. Review of Economic Dynamics 13, 637–653. doi: 10.1016/j.red.2009.06.002
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