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 where each seller has one kind of item that can be sold in whole to a buyer, and each buyer’s value can be represented by a single parameter, i.e., single-parameter setting, we develop a maximum mechanism for the market maker to maximize its own revenue. For the more general case where the product may be different, we consider various models in terms of supplies and demands constraints. 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.