A Simple and Approximately Optimal Mechanism for a Buyer with Complements: Abstract
A Simple and Approximately Optimal Mechanism for a Buyer with Complements: Abstract
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对于具有互补性的买方来说，一种简单且近似最优的机制：摘要
DOI：
10.1145/3033274.3085116
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Michal Feldman
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文献类型：
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作者：
Michal Feldman
我们考虑使用M Maximimimain的卖方和M的异质物品和一个单一买家，其价值V可能存在两个替代品（即，对于某些s，t，v（s∪t）<v（s） + v（s） + v（t） ）和完成（即，对于某些s，t，v（s t）> v（s） + v（t））。分别出售物品并将它们捆绑在一起 - 保证θ（d）最佳收入的一部分，其中$ d $是互补程度的衡量标准。这证明，当购买者值以下时，相同的简单机制达到了恒定的因子近似，这是最通用的完整值。二元框架在Cai等人[2016]中开发，我们用来在我们的主要技术中获得最佳收入。超图甚至钉住了“互补程度”的正确模型和概念，以获得有意义的结果，因为先前定义的自然扩展是正确的。
We consider a revenue-maximizing seller with m heterogeneous items and a single buyer whose valuation v for the items may exhibit both substitutes (i.e., for some S, T, v(S ∪ T) < v(S) + v(T)) and complements (i.e., for some S, T, v(S ∪ T) > v(S) + v(T)). We show that the mechanism first proposed by Babaioff et al. [2014] -- the better of selling the items separately and bundling them together -- guarantees a Θ(d) fraction of the optimal revenue, where $d$ is a measure on the degree of complementarity. Note that this is the first approximately optimal mechanism for a buyer whose valuation exhibits any kind of complementarity. It extends the work of Rubinstein and Weinberg [2015], which proved that the same simple mechanisms achieve a constant factor approximation when buyer valuations are subadditive, the most general class of complement-free valuations. Our proof is enabled by the recent duality framework developed in Cai et al. [2016], which we use to obtain a bound on the optimal revenue in this setting. Our main technical contributions are specialized to handle the intricacies of settings with complements, and include an algorithm for partitioning edges in a hypergraph. Even nailing down the right model and notion of "degree of complementarity" to obtain meaningful results is of interest, as the natural extensions of previous definitions provably fail.