论贸易最大化的多维收益
On Multi-Dimensional Gains from Trade Maximization
摘要：
我们研究了多维双边市场中的贸易收益。具体来说，我们专注于设置与$n$异构项目，其中每个项目是由不同的卖方$i$拥有，并有一个受约束的添加剂买方可行性约束$\mathcal{F}$。单边市场中的多维设置，例如卖方拥有多个异质项目，但也是机制设计者，是很好理解的。此外，双边市场中的单维设置，例如买方和卖方各自寻求或拥有单一物品，也很容易理解。然而，多维双边市场包含了两条工作线的主要挑战：优化异构项目的销售，确保市场双方之间的激励兼容性，以及执行预算平衡。我们目前，尽我们所知，第一个最坏情况下的近似保证，在一个多维的双边市场的贸易收益。我们的第一个结果提供了一个$O(\log (1/r))$近似的第一个最好的收益，从贸易的广泛类向下封闭的可行性约束（如拟阵，匹配，背包，或这些的交集）。这里，$r$是所有物品中买方的物品价值超过卖方成本的最小概率。我们的第二个结果消除了对$r$的依赖，并提供了一个无条件的$O(\log n)$ -近似的第二个最好的贸易收益。我们扩展这两个结果的一般约束添加剂的买家，失去另一个$O(\log n)$ -因素途中。
英文摘要：
We study gains from trade in multi-dimensional two-sided markets. Specifically, we focus on a setting with $n$ heterogeneous items, where each item is owned by a different seller $i$, and there is a constrained-additive buyer with feasibility constraint $\mathcal{F}$. Multi-dimensional settings in one-sided markets, e.g. where a seller owns multiple heterogeneous items but also is the mechanism designer, are well-understood. In addition, single-dimensional settings in two-sided markets, e.g. where a buyer and seller each seek or own a single item, are also well-understood. Multi-dimensional two-sided markets, however, encapsulate the major challenges of both lines of work: optimizing the sale of heterogeneous items, ensuring incentive-compatibility among both sides of the market, and enforcing budget balance. We present, to the best of our knowledge, the first worst-case approximation guarantee for gains from trade in a multi-dimensional two-sided market. Our first result provides an $O(\log (1/r))$-approximation to the first-best gains from trade for a broad class of downward-closed feasibility constraints (such as matroid, matching, knapsack, or the intersection of these). Here $r$ is the minimum probability over all items that a buyer's value for the item exceeds the seller's cost. Our second result removes the dependence on $r$ and provides an unconditional $O(\log n)$-approximation to the second-best gains from trade. We extend both results for a general constrained-additive buyer, losing another $O(\log n)$-factor en-route.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
