Cardinality Bundling with Spence-Mirrlees Reservation Prices




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Cardinality Bundling with Spence-Mirrlees Reservation Prices


Jianqing Wu

University of Washington

Jianqing “Fisher” Wu is an Assistant Professor in Information Systems at Foster School of Business, University of Washington. He received a PhD in Management Information Systems from Purdue University. He is interested in the research areas of Bundling, Pricing, Mobile Commerce, Information Security, Game Theory, and Convex Analysis. His teaching interests include Management Information Systems, Business Data Analytics, Optimization Model Spreadsheet, Database Management, Statistical and Econometric Models, Social Media, and E-Commerce. Jianqing Wu also received an MBA degree from Purdue University and a bachelor degree in Electronic Engineering from Shanghai Jiao Tong University.


We study the pricing of cardinality bundles, where firms set prices that depend only on the size of the purchased bundle, a practice that is increasingly being adopted by industry. The model we study, where consumer choices are discrete, was originally proposed by Hitt and Chen (2005) and it requires that consumers' preferences obey Spence-Mirrlees Single Crossing Property (SCP). We develop a fast combinatorial technique to obtain the optimal prices. We extend our analysis to address a quantity discount problem originally proposed in Spence (1980). We provide examples that demonstrate that the proposed approach of Spence (1980) only identifies local optima without providing guidance on selecting the globally optimal pricing function. Our insights from the discrete model are extended to this context to develop a scheme that provides solutions within an arbitrary pre-specified tolerance. Consequently, we also solve the continuous version of the cardinality bundling problem.