We explore the revenue capabilities of truthful, monotone (“fair”) allocation and pricing functions for resource constrained auction mechanisms within a general framework that encompasses unlimited supply auctions, knapsack auctions, and auctions with general non-decreasing convex production cost functions. We study and compare the revenue obtainable in each fair pricing scheme to the profit obtained by the ideal omniscient multi-price auction. We show that for capacitated knapsack auctions, no constant pricing scheme can achieve any approximation to the optimal profit, but proportional pricing is as powerful as general monotone pricing. In addition, for auction settings with arbitrary bounded non-decreasing convex production cost functions, we present a proportional pricing mechanism which achieves a poly-logarithmic approximation. Unlike existing approaches, all of our mechanisms have fair (monotone) prices, and all of our competitive analysis is with respect to the optimal profit extraction.
Chung, C., Ligett, K., Pruhs, K., & Roth, A. (2011). The power of fair pricing mechanisms. Algorithmica 63,3 (July, 2012), 634-644.
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