Revenue maximization in a Bayesian double auction market

We study double auction market design where the market maker wants to maximize its total revenue by buying low from the sellers and selling high to the buyers. We consider a Bayesian setting where buyers and sellers have independent probability distributions on the values of products on the market.For the simplest setting, each seller has one kind of indivisible good with a bounded (integer) amount that can be sold to a buyer, who may demand a bounded number of copies. We develop a maximum mechanism for the market maker to maximize its own revenue.For the more general case where each seller's product may be different, we consider a number of variants in terms of constraints on supplies and demands. For each of them, we develop a polynomial time computable truthful mechanism for the market maker to achieve a revenue at least a constant α times the revenue of any other truthful mechanism.