Minimax Regret Robust Screening with Moment Information

Shixin Wang (), Shaoxuan Liu () and Jiawei Zhang ()
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Shixin Wang: Department of Decisions, Operations and Technology, Chinese University of Hong Kong Business School, Chinese University of Hong Kong, Ma Liu Shui, Hong Kong
Shaoxuan Liu: Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China
Jiawei Zhang: Department of Technology, Operations & Statistics, Stern School of Business, New York University, New York, New York 10012

Manufacturing & Service Operations Management, 2024, vol. 26, issue 3, 992-1012

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.

Keywords: auctions and mechanism design; game theory; pricing and revenue management (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormsom:v:26:y:2024:i:3:p:992-1012

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