Linear payment rules for combinatorial exchanges

Internet technology has led to an increasing number of two-sided markets with many buyers and sellers involved. In many of these markets there is a need for package bids such that bidders can express preferences for sets of objects which might be complements or substitutes. Such combinatorial markets have found wide-spread application. There is a substantial literature in IS and other disciplines on payment rules in single-sided combinatorial auctions. However, payment rules for two-sided combinatorial auctions (aka. combinatorial exchanges) are largely unexplored. Linear and anonymous competitive equilibrium prices are desirable but unfortunately they do not always exist in non-convex markets. We discuss the market design for a large-scale combinatorial exchange for fishery access rights. The specifics of the allocation problem lead to different ways how linear and anonymous prices can be computed. We analyze trade-offs of different payment rules relevant to an auction designer.