Fixed-Price Approximations in Bilateral Trade

Fixed-Price Approximations in Bilateral Trade
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双边贸易中的固定价格近似值

DOI:
10.1137/1.9781611977073.115
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发表时间:
2022
期刊:
Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA
影响因子:
--
通讯作者:
Vondrák, Jan
Vondrák, Jan
中科院分区:
--
文献类型:
--
作者:
Kang, Zi Yang;Pernice, Francisco;Vondrák, Jan

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我们考虑双边贸易问题,其中两个代理商交易一个不可分割的项目。众所周知,唯一的优势策略真实机制是固定价格机制:给定买方价值和卖方价值S的普遍已知分布,如果S ≤p≤B,则向双方代理提供价格p,并发生交易。我们的目标是最大化期望福利或期望收益的贸易。我们改进了几个福利最大化的变量这个问题的近似比。当代理人的分布是相同的,我们证明了福利的最佳逼近比。只有一个先验样本的共同分布,我们表明,3/4近似福利是可以实现的。当代理人的分布不需要是相同的,我们表明,以前最有名的(1-1/e)-近似可以严格改进,但1-1/e是最佳的,如果只有卖方的分布是已知的。
We consider the bilateral trade problem, in which two agents trade a single indivisible item. It is known that the only dominant-strategy truthful mechanism is the fixed-price mechanism: given commonly known distributions of the buyer's valueBand the seller's valueS, a pricepis offered to both agents and trade occurs ifS≤p≤B. The objective is to maximize either expected welfare or expected gains from trade .We improve the approximation ratios for several welfare maximization variants of this problem. When the agents' distributions are identical, we show that the optimal approximation ratio for welfare is . With just one prior sample from the common distribution, we show that a 3/4-approximation to welfare is achievable. When agents' distributions are not required to be identical, we show that a previously best-known (1–1/e)-approximation can be strictly improved, but 1–1/eis optimal if only the seller's distribution is known.
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