Computing equilibria in markets with budget-additive utilities

• Main Authors: Garg, Jugal, Hoefer, Martin, Bei, Xiaohui, Mehlhorn, Kurt
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2018
• Subjects: Budget-Additive Utility; DRNTU::Science::Mathematics; Market Equilibrium
• Online Access: https://hdl.handle.net/10356/89959; http://hdl.handle.net/10220/47170
• Institution: Nanyang Technological University

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.