On competitiveness in uniform utility allocation markets

Authors:
Deeparnab Chakrabarty;Nikhil Devanur
Affiliations:
Department of Combinatorics and Optimization, University of Waterloo, Canada;Microsoft Research, Redmond, WA, USA
Venue:
Operations Research Letters
Year:
2009

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Abstract

We call a market competitive if increasing the endowment of one buyer does not increase the equilibrium utility of another. We show that every competitive uniform utility allocation market is a submodular utility allocation market, answering a question of Jain and Vazirani [K. Jain, V.V. Vazirani, Eisenberg-Gale markets: Algorithms and structural properties, in: STOC, 2007]. Our proof proceeds via characterizing non-submodular fractionally sub-additive functions.