On Competitiveness in Uniform Utility Allocation Markets

  • Deeparnab Chakrabarty
  • Nikhil Devanur

Operations Research Letters | , Vol 37: pp. 155-158

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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 allocationmarket 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.