Modularity and greed in double auctions

Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop a modular approach to the design of double auctions, by relating it to the exhaustively-studied problem of designing one-sided mechanisms with a single seller (or, alternatively, a single buyer). We consider several desirable properties of a double auction: feasibility, dominant-strategy incentive compatibility, the still stronger incentive constraints offered by a deferred-acceptance implementation, exact and approximate welfare maximization, and budget balance. For each of these properties, we identify sufficient conditions on two one-sided algorithms—one for ranking the buyers, one for ranking the sellers—and on a method for their composition into trading pairs, which guarantee the desired property of the double auction. Our framework also offers new insights into classic double auction designs, such as the VCG and McAfee auctions with unit-demand buyers and unit-supply sellers.