A Matter of Equality: Linear Pricing in Combinatorial Exchanges

Abstract

Combinatorial exchanges that allow for package offers to address nonconvexities in demand or supply typically employ linear and anonymous prices because they are simple, tractable, and fair. Despite their prevalence, linear anonymous prices do not necessarily correspond to Walrasian competitive equilibrium prices in such settings, and their impact is not well understood. This paper is the first to analyze the effect of different pricing rules on the efficiency of combinatorial exchanges, using both analytic methods and numerical experiments. Our analysis is motivated by a combinatorial fishery-rights exchange designed to reform the fishing industry in New South Wales (NSW), Australia. We find that when linearity and anonymity are required for only one side of the market, the average efficiency loss is negligible. In contrast, with a single linear price vector for both sides, the efficiency loss is substantial, especially when the market is small. In a formal model, we show that efficiency losses decrease when the number of buyers grows or the size of the submitted packages decreases. Besides the reform of the NSW fishing industry, our results have important implications for other cap-and-trade programs as well as other industries where demand or cost complementarities play a role.