Buyer Power, Exclusion, and Ine ¢ cient Trade

We consider a model in which multiple competing players trade with a sin-gle common player. As in models of common agency, we assume the competing players make contract o¤ers, which the common player accepts or rejects. How-ever, unlike models of common agency, we assume the competing players choose which quantities to trade. We show that when the competing playerspayo¤s are decreasing in the quantities of their rivals, in every equilibrium at least one competing player is excluded from trade with the common player. Exclusion occurs in equilibrium even though each players contract depends only on the quantity it trades and not on the quantities traded by its rivals. We also show that the players that trade in equilibrium may not be the most e ¢ cient players