Computing Equilibria in Markets with Budget-Additive Utilities

Authors Xiaohui Bei, Jugal Garg, Martin Hoefer, Kurt Mehlhorn

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Xiaohui Bei
Jugal Garg
Martin Hoefer
Kurt Mehlhorn

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Xiaohui Bei, Jugal Garg, Martin Hoefer, and Kurt Mehlhorn. Computing Equilibria in Markets with Budget-Additive Utilities. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization problems. They extend the standard case of linear utilities and have been studied in a variety of other market models. In contrast to the frequently studied CES utilities, they have a global satiation point which can imply multiple market equilibria with quite different characteristics. Our main result is an efficient combinatorial algorithm to compute a market equilibrium with a Pareto-optimal allocation of goods. It relies on a new descending-price approach and, as a special case, also implies a novel combinatorial algorithm for computing a market equilibrium in linear Fisher markets. We complement this positive result with a number of hardness results for related computational questions. We prove that it isNP-hard to compute a market equilibrium that maximizes social welfare, and it is PPAD-hard to find any market equilibrium with utility functions with separate satiation points for each buyer and each good.
  • Budget-Additive Utility
  • Market Equilibrium
  • Equilibrium Computation


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