Approximation algorithms and online mechanisms for item pricing

Abstract: We present approximation and online algorithms for problems of pricing a collection of items for sale so as to maximize the seller’s revenue in an unlimited supply setting. Our first result is an O(k)-approximation algorithm for pricing items to single-minded bidders who each want at most k items. This improves over work of Briest and Krysta (2006) who achieve an O(k2) bound. For the case k = 2, where we obtain a 4-approximation, this can be viewed as the following graph vertex pricing problem: given a (multi) graph G with valuations wi j on the edges, find prices pi ≥ 0 for the vertices to maximize {(i, j):wi j≥pi+p j} (pi + p j). We also improve the approximation of Guruswami et al. (2005) for the “highway problem” in which all desired subsets are intervals on a line, from O(logm+ logn) to O(logn), where m is the number of bidders and n is the number of items. Our approximation algorithms ca