{"title":"利用时刻信息进行最小回归稳健筛选","authors":"Shixin Wang, Shaoxuan Liu, Jiawei Zhang","doi":"10.1287/msom.2023.0072","DOIUrl":null,"url":null,"abstract":"Problem definition: We study a robust screening problem where a seller attempts to sell a product to a buyer knowing only the moment and support information of the buyer’s valuation distribution. The objective is to maximize the competitive ratio relative to an optimal hindsight policy equipped with full valuation information. Methodology/results: We formulate the robust screening problem as a linear programming problem, which can be solved efficiently if the support of the buyer’s valuation is finite. When the support of the buyer’s valuation is continuous and the seller knows the mean and the upper and lower bounds of the support for the buyer’s valuation, we show that the optimal payment is a piecewise polynomial function of the valuation with a degree of at most two. Moreover, we derive the closed-form competitive ratio corresponding to the optimal mechanism. The optimal mechanism can be implemented by a randomized pricing mechanism whose price density function is a piecewise inverse function adjusted by a constant. When the mean and variance are known to the seller, we propose a feasible piecewise polynomial approximation of the optimal payment function with a degree of at most three. We also demonstrate that the optimal competitive ratio exhibits a logarithmic decay with respect to the coefficient of variation of the buyer’s valuation distribution. Managerial implications: Our general framework provides an approach to investigating the value of moment information in the robust screening problem. We establish that even a loose upper bound of support or a large variance can guarantee a good competitive ratio. Funding: The research of S. Liu is partly supported by the National Natural Science Foundation of China [Grant NSFC-72072117]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0072 .","PeriodicalId":119284,"journal":{"name":"Manufacturing & Service Operations Management","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Minimax Regret Robust Screening with Moment Information\",\"authors\":\"Shixin Wang, Shaoxuan Liu, Jiawei Zhang\",\"doi\":\"10.1287/msom.2023.0072\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Problem definition: We study a robust screening problem where a seller attempts to sell a product to a buyer knowing only the moment and support information of the buyer’s valuation distribution. The objective is to maximize the competitive ratio relative to an optimal hindsight policy equipped with full valuation information. Methodology/results: We formulate the robust screening problem as a linear programming problem, which can be solved efficiently if the support of the buyer’s valuation is finite. When the support of the buyer’s valuation is continuous and the seller knows the mean and the upper and lower bounds of the support for the buyer’s valuation, we show that the optimal payment is a piecewise polynomial function of the valuation with a degree of at most two. Moreover, we derive the closed-form competitive ratio corresponding to the optimal mechanism. The optimal mechanism can be implemented by a randomized pricing mechanism whose price density function is a piecewise inverse function adjusted by a constant. When the mean and variance are known to the seller, we propose a feasible piecewise polynomial approximation of the optimal payment function with a degree of at most three. We also demonstrate that the optimal competitive ratio exhibits a logarithmic decay with respect to the coefficient of variation of the buyer’s valuation distribution. Managerial implications: Our general framework provides an approach to investigating the value of moment information in the robust screening problem. We establish that even a loose upper bound of support or a large variance can guarantee a good competitive ratio. Funding: The research of S. Liu is partly supported by the National Natural Science Foundation of China [Grant NSFC-72072117]. 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引用次数: 3
摘要
问题定义:我们研究的是一个稳健筛选问题,即卖方在只知道买方估值分布的时刻和支持信息的情况下,试图向买方出售产品。我们的目标是,相对于具备完整估值信息的最优后见之明政策,最大化竞争比率。方法/结果:我们将稳健筛选问题表述为一个线性规划问题,如果买方估值的支持度是有限的,这个问题就可以有效解决。当买方估值的支持是连续的,且卖方知道买方估值的平均值和支持的上下限时,我们证明最优付款是估值的一次多项式函数,度数最多为 2。此外,我们还推导出了与最优机制相对应的闭式竞争比率。最优机制可以通过随机定价机制来实现,该机制的价格密度函数是一个由常数调整的片断反函数。当卖方已知均值和方差时,我们提出了一个可行的片断多项式近似最优支付函数,度数最多为三。我们还证明,最优竞争比率与买方估值分布的变异系数呈对数衰减关系。管理意义:我们的一般框架为研究稳健筛选问题中时刻信息的价值提供了一种方法。我们发现,即使是宽松的支持上限或较大的方差也能保证良好的竞争比率。资助:S. Liu 的研究得到了国家自然科学基金[NSFC-72072117]的部分资助。补充材料:在线附录见 https://doi.org/10.1287/msom.2023.0072 。
Minimax Regret Robust Screening with Moment Information
Problem definition: We study a robust screening problem where a seller attempts to sell a product to a buyer knowing only the moment and support information of the buyer’s valuation distribution. The objective is to maximize the competitive ratio relative to an optimal hindsight policy equipped with full valuation information. Methodology/results: We formulate the robust screening problem as a linear programming problem, which can be solved efficiently if the support of the buyer’s valuation is finite. When the support of the buyer’s valuation is continuous and the seller knows the mean and the upper and lower bounds of the support for the buyer’s valuation, we show that the optimal payment is a piecewise polynomial function of the valuation with a degree of at most two. Moreover, we derive the closed-form competitive ratio corresponding to the optimal mechanism. The optimal mechanism can be implemented by a randomized pricing mechanism whose price density function is a piecewise inverse function adjusted by a constant. When the mean and variance are known to the seller, we propose a feasible piecewise polynomial approximation of the optimal payment function with a degree of at most three. We also demonstrate that the optimal competitive ratio exhibits a logarithmic decay with respect to the coefficient of variation of the buyer’s valuation distribution. Managerial implications: Our general framework provides an approach to investigating the value of moment information in the robust screening problem. We establish that even a loose upper bound of support or a large variance can guarantee a good competitive ratio. Funding: The research of S. Liu is partly supported by the National Natural Science Foundation of China [Grant NSFC-72072117]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0072 .