How to Allocate Goods in an Online Market?

Abstract. We study an online version of Fisher's linear case market. In this market there are m buyers and a set of n dividable goods to be allocated to the buyers. The utility that buyer i derives from good j is uij. Given an allocation ^U in which buyer i has utility ^Ui we suggest a quality measure that is based on taking an average of the ratios Ui/ ^Ui with respect to any other allocation U. We motivate this quality measure, and show that market equilibrium is the optimal solution with respect to this measure. Our setting is online and so the allocation of each good should be done without any knowledge of the upcoming goods. We design an online algorithm for the problem that is only worse by a logarithmic factor than any other solution with respect to our proposed quality measure, and in particular competes with the market equilibrium allocation. We prove a tight lower bound which shows that our algorithm is optimal up to constants. Our algorithm uses a primal dual convex pro...

• Type: Journal
• Year: 2010
• Where: ESA
• Authors: Yossi Azar, Niv Buchbinder, Kamal Jain
• Keywords: Algorithms, Buyer, ESA 2010, Market, Quality Measure