Algorithmic pricing is the computational problem that sellers (e.g., in supermarkets) face when trying to set prices for their items to maximize their profit in the presence of a known demand. Guruswami et al. (2005) propose this problem and give logarithmic approximations (in the number of consumers) when each consumer's values for bundles are known precisely. Subsequently several versions of the problem have been shown to have poly-logarithmic inapproximability. This problem has direct ties to the important open question of better understanding the Bayesian optimal mechanism in multi-parameter settings; however, logarithmic approximations are inadequate for this purpose. It is therefore of vital interest to consider special cases where constant approximations are possible. We consider the unit-demand variant of this problem. Here a consumer has a valuation for each different item and their value for a set of items is simply the maximum value they have for any item in the set. We assume that the preferences of the consumers are drawn from a distribution, the standard assumption in economics; furthermore, the setting of a specific set of customers with known preferences, which is employed in all prior work in algorithmic pricing, is a special case of this general problem, where there is a discrete Bayesian distribution for preferences specified by picking one consumer uniformly from the given set of consumers. Our work complements these existing works by considering the case where the consumer's valuations for the different items are independent random variables. Our main result is a constant approximation that makes use of an interesting connection between this problem and the concept of virtual valuations from the single-parameter Bayesian optimal mechanism design literature.
From Stream to Pool: Pricing Under the Law of Diminishing Marginal Utility
Joseph M. Katz Graduate School of Business, University of Pittsburgh（匹兹堡大学约瑟夫·M·卡茨商学院）；Center of Data Science for Enterprise and Society (CDSES), Cornell University（康奈尔大学企业与社会数据科学中心）；Naveen Jindal School of Management, UT Dallas（德克萨斯大学达拉斯分校纳文·金达尔管理学院）
Simplicity in Auctions Revisited: The Primitive Complexity
在本文中，我们重新审视机制的简单性的概念。我们考虑一个$m$物品的卖家，面对一个估价为$v$的买家。我们观察到，以前定义复杂性度量的尝试通常无法对直观上认为简单的机制进行分类（例如，“单独销售”机制）。我们建议将菜单视为简单的，如果可以通过执行一些被认为简单的原始操作来找到最大化买方利润的捆绑包。\emph{primitive complexity of a menu}是在菜单中（自适应地）找到利润最大化条目所需的基本操作的数量。在本文中，我们研究的原始操作本质上是计算“分别销售”机制的结果。这种原始的复杂性是否体现了其他拍卖的简单性？我们考虑\emph{bundle-size pricing}，一种常见的定价方法，其中捆绑包的价格仅取决于其大小。我们的主要技术贡献是确定了各种设置中的桌面大小定价菜单的原始复杂性。我们发现，任何分布$\cal D$加权拟阵秩估值，甚至分布与任意相关的值，总是有一个低原始复杂性，实现几乎相同的收入，最佳的尺寸尺寸定价菜单的尺寸定价菜单。作为这个证明的一部分，我们提供了一个随机算法，对于任何加权拟阵秩估值$v$和整数$k$，发现最有价值的一组大小$k$只有一个多对数的需求和值查询。我们表明，这一结果在几个方面基本上是紧的。例如，如果赋值$v$是次模的，则找到大小为$k$的最有价值的集合需要指数地多次查询（这解决了Badanidiyuru等人的公开问题[…
a pawfessor of economics and of computer science（经济与计算机科学教授）；OpenAI’s Researcher Access Program（OpenAI研究员访问计划）；Google’s Gemini Academic Program（Google的Gemini学术计划）；Cloud Research Credits Program（云研究信用计划）；Anthropic；NSF Graduate Research Fellowship（NSF研究生研究 fellowship）；Kempner Institute Graduate Fellowship（Kempner研究所研究生 fellowship）；National Science Foundation (NSF-BSF grant No. 2343922)（国家科学基金会（NSF-BSF grant No. 2343922））；Harvard FAS Dean’s Competitive Fund for Promising Scholarship（哈佛大学哈佛大学教务处有前途的学术研究竞争基金）；Harvard FAS Inequality in America Initiative（哈佛大学哈佛大学美国不平等倡议）；United States–Israel Binational Science Foundation (BSF grant 2022417)（美国-以色列双边科学基金会（BSF grant 2022417））
