Menu-size Complexity and Revenue Continuity of Buy-many Mechanisms
Menu-size Complexity and Revenue Continuity of Buy-many Mechanisms
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多买机制的菜单规模复杂性和收入连续性
DOI：
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Christos Tzamos
中科院分区：
文献类型：
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作者：
Shuchi Chawla;Yifeng Teng;Christos Tzamos
研究了一个垄断者向单个购买者销售n个异质商品的多项目机制设计问题。在最近的工作中，Chawla等人主张研究所谓“买多”约束下的多项目机制的收益最大化。非正式地说，如果允许买方多次参与该机制，则该机制是多买多买的。例如，对购买商品子集感兴趣的购买者可以单独购买该子集的组件。将该机制视为为分配分配分配价格的函数，买多约束本质上等同于价格的次加性约束。买多约束是大多数现实世界机制都满足的自然属性。文献中所研究的简单类机制，如项目定价、大捆绑定价、两部分定价等，也都满足这一性质。因此，买多机制是一个值得研究的对象。Chawla等人询问buy-many机制是否表现出任意机制所不具备的结构特性。本文研究了两个这样的性质：菜单大小复杂性和收入连续性。我们讨论这两个性质，它们的意义和我们的结果。
We study the multi-item mechanism design problem where a monopolist sells n heterogeneous items to a single buyer. In recent work, Chawla et al. [2] advocated studying revenue maximization of multi-item mechanisms under the so-called "buy-many" constraint. Informally, a mechanism is buy-many if the buyer is allowed to participate in the mechanism any number of times. For example, a buyer interested in purchasing a subset of items may purchase the components of this subset individually. Viewing the mechanism as a function that assigns prices to allocations, the buy-many constraint is essentially equivalent to a subadditivity constraint over the prices. The buy-many constraint is a natural property that most real-world mechanisms satisfy. All of the simple classes of mechanisms studied in the literature such as item pricing, grand bundle pricing, two part tariffs, etc. also satisfy this property. As such, buy-many mechanisms are a worthy object of study. Chawla et al. asked whether buy-many mechanisms exhibit structural properties that arbitrary mechanisms do not. In this paper we study two such properties: menu-size complexity and revenue continuity. We discuss these two properties, their significance, and our results.
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