一种超越可加估值的分配博弈算法
An Algorithm for the Assignment Game Beyond Additive Valuations
AI总结：
研究超越原始假设的分配博弈，核心方法是结合最大匹配增广树技术和拟阵交算法，主要贡献是给出计算竞争均衡的高效算法，还证明两种推广模型下计算竞争均衡是NP难的。
摘要：
由Shapley和Shubik（1971）引入的分配博弈是买卖双方双边匹配市场的经典模型。原始模型假设支付导致可转移效用且买家对物品有单位需求估值。已有工作研究了更一般的不可完美转移效用和总替代估值设置。本文给出计算此类设置下竞争均衡的高效算法，并证明两种推广模型下计算竞争均衡是NP难的。
英文摘要：
The assignment game, introduced by Shapley and Shubik (1971), is a classic model for two-sided matching markets between buyers and sellers. In the original assignment game, it is assumed that payments lead to transferable utility and that buyers have unit-demand valuations for items. Two important and mostly independent lines of work have studied more general settings with imperfectly transferable utility and gross substitutes valuations. Multiple efficient algorithms have been proposed for computing a competitive equilibrium, the standard solution concept in assignment games, in these two settings. Our main result is an efficient algorithm for computing competitive equilibria in a setting with both imperfectly transferable utility and gross substitutes valuations. Our algorithm combines augmenting tree techniques from maximum matching and algorithms for matroid intersection. We also show that, in two mild generalizations of our model, computing a competitive equilibrium is NP-hard.
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。
