We consider the problem of maximizing the gains from trade (GFT) in two-sided markets. The seminal impossibility result by Myerson shows that even for bilateral trade, there is no individually rational (IR), Bayesian incentive compatible (BIC) and budget balanced (BB) mechanism that can achieve the full GFT. Moreover, the optimal BIC, IR and BB mechanism that maximizes the GFT is known to be complex and heavily depends on the prior. In this paper, we pursue a Bulow-Klemperer-style question, i.e. does augmentation allow for prior-independent mechanisms to beat the optimal mechanism? Our main result shows that in the double auction setting with $m$ i.i.d. buyers and $n$ i.i.d. sellers, by augmenting $O(1)$ buyers and sellers to the market, the GFT of a simple, dominant strategy incentive compatible (DSIC), and prior-independent mechanism in the augmented market is least the optimal in the original market, when the buyers' distribution first-order stochastically dominates the sellers' distribution. Furthermore, we consider general distributions without the stochastic dominance assumption. Existing hardness result by Babaioff et al. shows that no fixed finite number of agents is sufficient for all distributions. In the paper we provide a parameterized result, showing that $O(log(m/rn)/r)$ agents suffice, where $r$ is the probability that the buyer's value for the item exceeds the seller's value.

翻译：本文研究双边市场中交易收益最大化的优化问题。Myerson提出的经典不可能性结果表明，即使在双边交易中，也不存在同时满足个体理性、贝叶斯激励相容和预算平衡且能实现完全交易收益的机制。此外，已知最大化交易收益的最优BIC、IR和BB机制结构复杂且高度依赖于先验分布。本文探讨一个类似于Bulow-Klemperer风格的问题：增加市场参与方是否能使与先验无关的机制超越最优机制？我们的主要结论表明：在包含$m$个独立同分布买家和$n$个独立同分布卖家的双向拍卖场景中，若买家的价值分布一阶随机占优于卖家的价值分布，则通过在市场中增加$O(1)$个买家和卖家，采用一种简单、占优策略激励相容且与先验无关的机制所能实现的交易收益，至少不低于原始市场中最优机制所能实现的交易收益。进一步地，我们考虑不满足随机占优假设的一般分布情形。Babaioff等人的既有困难性结果表明，不存在固定有限数量的代理人能适用于所有分布。本文提出了一个参数化结果，证明当$r$表示买家对物品的估值超过卖家估值的概率时，增加$O(\log(m/rn)/r)$个代理人即足以满足要求。