近似高效的多维双边贸易
Approximately Efficient Multidimensional Bilateral Trade
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中文总结 AI 辅助
本文针对市场双方均为多维的双边贸易问题，在两类场景下提出满足BIC、IIR和事前WBB的简单机制，实现最优期望贸易收益的常数比例，突破了现有结果多适用于单维主体的限制。
中文摘要 AI 辅助
机制设计的核心挑战是开发能最大化双边市场中期望贸易收益（GFT）的真实贸易机制。由于实现完全GFT通常不可能，相关研究聚焦于常数因子近似——即使在简单场景中这也是个公认的难题。直到最近，[DMSW22]取得突破性成果，实现了单物品双边贸易的常数因子近似，该保证随后被扩展到具有一般向下闭包约束的单维匹配市场[BRTW26]。然而，现有多数结果仅适用于单维主体，一个值得注意的多维例外是[CGMZ21]，他们考虑了一个包含1个受约束加性买方和n个单维卖方的市场，提供的机制对次优GFT（即满足贝叶斯激励相容（BIC）、中期个体理性（IIR）和事前弱预算平衡（WBB）的机制在理论上可实现的最大期望GFT）达到log²(n)的近似。本文研究市场双方均为多维的多维双边贸易问题：从1个具有XOS估值的买方和1个具有加性成本函数的卖方开始，再推广到包含n个XOS买方和1个加性卖方的市场，在假设各物品的价值与成本相互独立的前提下，针对两种场景均提出了满足BIC、IIR和事前WBB的简单机制，同时实现了最优（第一优）期望GFT的常数比例。
英文摘要
A central challenge in mechanism design is to develop truthful trade mechanisms that maximize the expected gains-from-trade (GFT) in two-sided markets. Because achieving the full GFT is generally impossible, the literature has focused on constant-factor approximations---a notoriously difficult problem even in simple settings. It was only recently that a breakthrough result by [DMSW22] achieved a constant-factor approximation for single-item bilateral trade. The same guarantee was later extended to single-dimensional matching markets with general downward-closed constraints [BRTW26]. Most existing results, however, are limited to single-dimensional agents. A notable multi-dimensional exception is [CGMZ21]. They considered a market with one constrained-additive buyer and $n$ single-dimensional sellers and provided a mechanism that achieves a $\log^2(n)$ approximation to the second-best GFT, i.e., the maximum expected GFT theoretically achievable by any mechanism satisfying Bayesian Incentive Compatibility (BIC), Interim Individual Rationality (IIR), and ex-ante Weak Budget Balance (WBB). In this paper, we study multi-dimensional bilateral trade problem where both sides of the market are multi-dimensional. We start with one buyer with XOS valuation and one seller with an additive cost function. We then generalize to a market with $n$ XOS buyers and one additive seller. Assuming independent items' values and costs, in both settings we propose simple mechanisms that are BIC, IIR, and ex-ante WBB, while achieving a constant fraction of the optimal (first-best) expected GFT.
发表机构
- Stanford University（斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。
