Mechanisms for a spatially distributed market

We consider the problem of a spatially distributed market with strategic agents. In this problem a single good is traded in a set of independent markets, where shipment between markets is possible but incurs a cost. The problem has previously been studied in the non-strategic case, in which it can be analyzed and solved as a min-cost-flow problem. We consider the case where buyers and sellers are strategic. Our first result gives a double characterization of the VCG prices, first as distances in a certain residue graph and second as the minimal (for buyers) and maximal (for sellers) equilibrium prices. This provides a computationally efficient, individually rational and incentive compatible welfare maximizing mechanism. This mechanism is, necessarily, not budget balanced and we provide also a budget-balanced mechanism (which is also computationally efficient, incentive compatible, and individually rational) that achieves high welfare. Some of our results extend to the cases where buyers and sellers have arbitrary convex demand and supply functions and to the case where transportation is controlled by strategic agents as well.