We study robust versions of pricing problems where customers choose products according to a generalized extreme value (GEV) choice model, and the choice parameters are not known exactly but lie in an uncertainty set. We show that, when the robust problem is unconstrained and the price sensitivity parameters are homogeneous, the robust optimal prices have a constant markup over products, and we provide formulas that allow to compute this constant markup by bisection. We further show that, in the case that the price sensitivity parameters are only homogeneous in each partition of the products, under the assumption that the choice probability generating function and the uncertainty set are partition-wise separable, a robust solution will have a constant markup in each subset, and this constant-markup vector can be found efficiently by convex optimization. We provide numerical results to illustrate the advantages of our robust approach in protecting from bad scenarios. Our results hold for convex and bounded uncertainty sets,} and for any arbitrary GEV model, including the multinomial logit, nested or cross-nested logit.
Learning Choice Model Trees for Feature-Based Multi-Product Pricing: Exact Optimization and Field Evidence
Institute of Operations Research and Analytics, National University of Singapore（新加坡国立大学运筹与分析研究所）；NUS Business School, National University of Singapore（新加坡国立大学商学院）
Decentralized Multi-product Pricing: Diagonal Dominance, Nash Equilibrium, and Price of Anarchy
Department of Information & Decision Sciences, College of Business Administration, University of Illinois Chicago（伊利诺伊大学芝加哥分校商学院信息与决策科学系）；Department of Industrial Engineering & Decision Analytics, The Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析系）；Department of Technology and Operations, Ross School of Business, University of Michigan（密歇根大学罗斯商学院技术与运营系）
Optimal Online and Offline Algorithms for Contextual MNL with Applications to Assortment and Pricing
Stern School of Business, New York University（纽约大学斯特恩商学院）；China Europe International Business School (CEIBS)（中欧国际工商学院）；Department of Management Science & Engineering, Stanford University（斯坦福大学管理科学与工程系）
