Approximating Gains from Trade in Two-sided Markets via Simple Mechanisms

We design simple mechanisms to approximate the Gains from Trade (GFT) in two-sided markets with multiple unit-supply sellers and multiple unit-demand buyers. A classical impossibility result by Myerson and Satterthwaite showed that even with only one seller and one buyer, no Bayesian Incentive Compatible (BIC), Individually Rational (IR), and Budget-Balanced (BB) mechanism can achieve full GFT (trade whenever buyer's value is higher than the seller's cost). The same paper also proposed the ``second-best'' mechanism that maximizes the GFT subject to BIC, IR, and BB constraints, which is unfortunately rather complex for even the single-seller single-buyer case. Our mechanism is simple, BIC, IR, and BB and achieves 1/2 of the optimal GFT among all BIC, IR, and BB mechanisms. The result holds for arbitrary distributions of the buyers' and sellers' values and can accommodate any downward-closed feasibility constraints over the allocations. The analysis of our mechanism is facilitated by extending the Cai-Weinberg-Devanur duality framework to two-sided markets.

我们设计了简单的机制，以近似具有多个单位供应商和多个单位需求购买者的双面市场的贸易收益（GFT）。 Myerson和Satterthwaite的经典不可能结果表明，即使只有一个卖方和一个买家，也没有贝叶斯激励兼容（BIC），个人合理（IR）和预算均衡（BB）机制可以实现全GFT（每当买家的价值时高于卖方的费用）。同一篇论文还提出了``第二好的''机制，该机制使GFT最大化受BIC，IR和BB约束，但不幸的是，即使是单价单销售商的单个案例，这也是相当复杂的。我们的机制简单，BIC，IR和BB，并且在所有BIC，IR和BB机制中达到了最佳GFT的1/2。结果适用于买方和卖方价值的任意分配，并且可以适应对分配的任何向下封闭的可行性约束。通过将Cai-Weinberg-Devanur二重性框架扩展到双面市场，可以促进我们机制的分析。