We study the problem of designing a two-sided market (double auction) to maximize the gains from trade (social welfare) under the constraints of (dominant-strategy) incentive compatibility and budget-balance. Our goal is to do so for an unknown distribution from which we are given a polynomial number of samples. Our first result is a general impossibility for the case of correlated distributions of values even between just one seller and two buyers, in contrast to the case of one seller and one buyer (bilateral trade) where this is possible. Our second result is an efficient learning algorithm for one seller and two buyers in the case of independent distributions which is based on a novel algorithm for computing optimal mechanisms for finitely supported and explicitly given independent distributions. Both results rely heavily on characterizations of (dominant-strategy) incentive compatible mechanisms that are strongly budget-balanced.

翻译：我们研究设计双边市场（双重拍卖）以最大化交易收益（社会福利）的问题，同时满足（占优策略）激励相容和预算平衡的约束。我们的目标是在仅获得多项式数量样本的情况下，针对未知分布实现这一目标。我们的第一个结果表明，即使仅涉及一个卖家和两个买家，在价值分布相关的情况下普遍存在不可能性，这与一个卖家和单个买家（双边交易）的情况形成对比，后者是可能实现的。我们的第二个结果是针对一个卖家和两个买家在独立分布情况下的高效学习算法，该算法基于一种新颖的计算最优机制的方法，适用于有限支撑且明确给定的独立分布。这两项结果都严重依赖于对满足强预算平衡的（占优策略）激励相容机制的刻画。