We develop a novel model of price-fee competition in bilateral oligopoly markets with non-expandable infrastructures and costly transportation. The model captures a variety of real market situations and it is the continuous quantity version of the assignment game with indivisible goods on a fixed network. We define and characterize stable market outcomes. Buyers exclusively trade with the supplier with whom they achieve maximal bilateral joint welfare at prices equal to marginal costs. Maximal fees and the suppliers’ market power are restricted by the buyers’ credible threats to switch suppliers. Maximal fees also arise from a negotiation model that extends price competition to price-fee competition. Competition in both prices and fees necessarily emerges. It improves welfare compared to price competition, but buyers will not be better off. The minimal infrastructure achieving maximal aggregate welfare differs from the minimal network that protects buyers most.
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