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作者：Chen, Xi; Lyu, Jiameng; Zhang, Xuan; Zhou, Yuan
作者单位：New York University; Fudan University; University of Illinois System; University of Illinois Urbana-Champaign; Tsinghua University
摘要：Price discrimination, which refers to the strategy of setting different prices for different customer groups, has been widely used in online retailing. Although it helps boost the collected revenue for online retailers, it might create serious concerns about fairness, which even violates regulations and laws. This paper studies the problem of dynamic discriminatory pricing under a relative price fairness constraint in the pricing literature. We first establish a regret lower bound of ohm(T4=5)...
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作者：Jia, Su; Li, Andrew; Ravi, R.; Oli, Nishant; Duff, Paul; Anderson, Ian
作者单位：Amazon.com; Carnegie Mellon University
摘要：Modern platforms leverage randomized experiments to make informed decisions from a given set of items (treatment arms). As a particularly challenging scenario, these items can (i) arrive in a high volume, with thousands of new items being released per hour, and (ii) have a short lifetime due to their transient nature. We study a Bayesian multiple-play bandit problem that encapsulates the key features of this scenario. In each round, a set of arms arrives. Each arm has a lifetime w and an unkno...
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作者：Jiang, Songchen; Li, Zhaolin; Bi, Sheng; Teo, Chung-Piaw; Huang, Min
作者单位：Northeastern University - China; National University of Singapore; University of Sydney; Shanghai University of Finance & Economics
摘要：We generalize Scarf's classical min-max newsvendor model from a singleperiod setting to a multiperiod inventory system with independent demand across periods. This extension leverages mean-variance analysis to capture the dynamic effects of lead times, yielding closed-form expressions for the optimal base-stock level. As a concrete application, we study a single-product, dual-sourcing system with constant lead times and backlogging. We show that the optimal tailored base-surge policy admits a ...
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作者：Wang, Tong; Xiao, Li; Xu, Fen
作者单位：City University of Hong Kong; University of Macau; Huazhong University of Science & Technology
摘要：This paper establishes two new preservation results of multimodularity for two classes of resource allocation problems, where multiple resources can be used to satisfy multiple demands. Our results show that if allocation priorities between multiple resources and demands are determined by several marginal cost/value inequalities of the objective function, then the multimodularity and marginal cost/value inequalities are both preserved after optimization. We demonstrate their applications to se...
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作者：Xu, Zhandong; Li, Zhengyang; Xie, Jun; Chen, Anthony; Liu, Xiaobo
作者单位：Southwest Jiaotong University; Hong Kong Polytechnic University
摘要：This study generalizes the single-class traffic assignment problem of Nikolova and Stier-Moses [Nikolova and Stier-Moses (2014) A mean-risk model for the traffic assignment problem with stochastic travel times. Oper. Res. 62(2):366-382] by considering the continuously distributed risk-aversion factor, termed the continuous mean-risk traffic assignment (CMRTA) problem. In CMRTA, travelers categorized into infinitely many user classes play a congestion routing game based on their risk attitude t...
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作者：Han, Jiangze; Ryan, Christopher Thomas; Tong, Xin T.
作者单位：Columbia University; University of British Columbia; National University of Singapore
摘要：Loot boxes are a primary source of revenue in the video game industry. Loot boxes randomly drop items of differing value. To design a loot box, sellers must choose the loot box's purchase price and drop rate (or drop probability) of each item. We show that, in general, the loot box design problem is NP-hard. By restricting the form of player utilities, we can solve the problem exactly in polynomial time when the number of items is fixed. Under different restrictions, we solve the problem appro...
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作者：Abdelhakmi, Anas; Lim, Andrew E. B.
作者单位：National University of Singapore; National University of Singapore; National University of Singapore
摘要：The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the investor. We consider a generalization where the investor trades dynamically and views can be over horizons that differ from the investor. By exploiting the underlying graphical structure relating the asset prices and views, we derive the conditional distribu...
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作者：Deza, Anna; Hall, Georgina
作者单位：INSEAD Business School
摘要：We introduce the notion of t-sum of squares (sos) submodularity, which is a hierarchy, indexed by t, of sufficient algebraic conditions for certifying submodularity of set functions. We show that, for fixed t, each level of the hierarchy can be verified via a semidefinite program of size polynomial in n, the size of the ground set of the set function. This is particularly relevant given existing results by Crama around testing whether a set function is submodular. We derive several equivalent ...
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作者：Abdallah, Tarek; Reed, Josh
作者单位：Northwestern University; New York University
摘要：We study the single-item dynamic pricing problem in three separate asymptotic regimes characterized by their ratio of inventory to market size. We first consider the case of customer item valuations following an exponential distribution, for which we derive a sharp characterization of the boundaries between each of the regimes. We then proceed to the case of customer item valuations following a general distribution. In this case, we derive for each regime approximations to the optimal value fu...
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作者：Golz, Paul; Peters, Dominik; Procaccia, Ariel D.
作者单位：University of California System; University of California Berkeley; Cornell University; Centre National de la Recherche Scientifique (CNRS); Harvard University
摘要：Apportionment is the problem of distributing h indivisible seats across states in proportion to the states' populations. In the context of the U.S. House of Representatives, this problem has a rich history and is a prime example of interactions between mathematical analysis and political practice. Grimmett suggests to apportion seats in a randomized way such that each state receives exactly its proportional share qi of seats in expectation (ex ante proportionality) and receives either left per...
