Endogenous Prices in Dense Transshipment Networks

Abstract

This paper analyzes optimal dealer pricing in dense dealer trade networks. A homogeneous linking network is developed where each link represents a trade relationship. The trade relationships are governed by an incentive compatibility constraint. The dealer obtaining the model through trade cannot charge the buyer so much that he is better off traveling for the model rather than obtaining it locally through trade. Informally, dense networks are defined to be networks with many nodes. A key insight of the paper is that prices become much easier to analyze as the network becomes dense. Further, the optimal price to charge the distant traveling buyer converges to a fixed value, regardless of network structure. This paper contributes to the transshipment literature in a multitude of ways. First, the paper analyzes optimal pricing as the number of trade relationships changes. Other papers in the literature compare networks with either no trade or complete trade. Second, the incentive compatibility constraint is a novel contribution. Third, the dealer sets three prices simultaneously; the price for the model in stock, the price for a model obtained through trade, and the price to lure the distant buyer. Other papers have not allowed the buyer to advertise different prices in different locations. Finally, existence of pairwise stable equilibrium is proved for dense networks. This and the results on optimal pricing could be used to further determine the optimal number of trade relationships, and thus could provide a better understanding of dealer trade policy than currently exists in the literature.