SIAM J. on Computing

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Print: 0097-5397
Electronic: 1095-7111
Coden: SMJCAT

The SIAM Journal on Computing contains research articles on the mathematical and formal aspects of computer science and nonnumerical computing. Topics include analysis and design of algorithms, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.

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Buying Cheap Is Expensive: Approximability of Combinatorial Pricing Problems

We investigate nonparametric multiproduct pricing problems, in which we want to find revenue maximizing prices for products $\mathcal{P}$ based on a set of customer samples $\mathcal{C}$. We mostly focus on the unit-demand case, in which products constitute strict substitutes and each customer aims to purchase a single product. In this setting a customer sample consists of a number of nonzero values for different products and possibly an additional product ranking. Once prices are fixed, each customer chooses to buy one of the products she can afford based on some predefined selection rule. We distinguish between the min-buying, max-buying, and rank-buying models. Some of our results also extend to single-minded pricing, in which case products are strict complements and every customer seeks to buy a single set of products, which she purchases if the sum of prices is below her valuation for that set.

SIAM J. Comput. 40, pp. 1554-1586