Incentive ratios of fisher markets

Authors:
Ning Chen;Xiaotie Deng;Hongyang Zhang;Jie Zhang
Affiliations:
Division of Mathematical Sciences, Nanyang Technological University, Singapore;Department of Computer Science, University of Liverpool, UK;Department of Computer Science, Shanghai Jiao Tong University, China;Department of Computer Science, Aarhus University, Denmark
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Year:
2012

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Abstract

In a Fisher market, a market maker sells m items to n potential buyers. The buyers submit their utility functions and money endowments to the market maker, who, upon receiving submitted information, derives market equilibrium prices and allocations of its items. While agents may benefit by misreporting their private information, we show that the percentage of improvement by a unilateral strategic play, called incentive ratio, is rather limited--it is less than 2 for linear markets and at most $e^{1/e}\thickapprox 1.445$ for Cobb-Douglas markets. We further prove that both ratios are tight.