Item pricing for revenue maximization

Maria-Florina Balcan, Avrim Blum, Yishay Mansour
2008 ACM SIGecom Exchanges  
We consider the problem of pricing items to maximize revenue when faced with buyers with complex preferences, and show that a simple and natural pricing scheme achieves surprisingly strong guarantees. Our pricing scheme immediately implies approximation bounds for revenue maximization in general combinatorial auctions, both in the limited and unlimited supply settings. We show that in the unlimited supply setting, a random single price achieves expected revenue within a logarithmic factor of
more » ... total social welfare for customers with general valuation functions, which may not even necessarily be monotone. This generalizes work of Guruswami et. al [18] , who show a logarithmic factor for only the special cases of single-minded and unit-demand customers. In the limited supply setting, we consider natural classes of valuations functions that have been studied in the context of social welfare maximization: submodular, XOS, and more generally, subadditive valuation functions [14, 10, 12, 4] . We show here that a random single price achieves revenue within a 2 O( √ log n log log n) factor of the total social welfare, i.e., the optimal revenue the seller could hope to extract even if the seller could price each bundle differently for every buyer. This is the best approximation known for any item pricing scheme. We complement this result with a nearly matching lower bound showing a sequence of subadditive (in fact, XOS) buyers for which any single price has approximation ratio Ω(2 log 1/4 n ). This lower bound demonstrates a clear distinction between revenue maximization and social welfare maximization in this setting, for which [12, 10] show that a fixed price achieves a logarithmic approximation in the case of XOS [12] , and more generally subadditive [10], customers. We also consider the multi-unit case setting examined by [11] in the context of social welfare, and show that so long as no buyer requires nearly all the items, in this case a random single price does in fact achieve revenue within an O(log n) factor of the maximum social welfare.
doi:10.1145/1486877.1486883 fatcat:vxzqg5l6rvcslaq2sozqgzdcwq