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Computing Equilibria in Markets with Budget-Additive Utilities

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons134143

Bei,  Xiaohui
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons134167

Garg,  Jugal
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44628

Hoefer,  Martin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Volltexte (frei zugänglich)

arXiv:1603.07210.pdf
(Preprint), 603KB

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Zitation

Bei, X., Garg, J., Hoefer, M., & Mehlhorn, K. (2016). Computing Equilibria in Markets with Budget-Additive Utilities. Retrieved from http://arxiv.org/abs/1603.07210.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-002A-FCC0-C
Zusammenfassung
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 these positive results with a number of hardness results for related computational questions. We prove that it is NP-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.