Liquid price of anarchy

Yossi Azar, Michal Feldman, Nick Gravin, Alan Roytman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Incorporating budget constraints into the analysis of auctions has become increasingly important, as they model practical settings more accurately. The social welfare function, which is the standard measure of efficiency in auctions, is inadequate for settings with budgets, since there may be a large disconnect between the value a bidder derives from obtaining an item and what can be liquidated from her. The Liquid Welfare objective function has been suggested as a natural alternative for settings with budgets. Simple auctions, like simultaneous item auctions, are evaluated by their performance at equilibrium using the Price of Anarchy (PoA) measure – the ratio of the objective function value of the optimal outcome to the worst equilibrium. Accordingly, we evaluate the performance of simultaneous item auctions in budgeted settings by the Liquid Price of Anarchy (LPoA) measure – the ratio of the optimal Liquid Welfare to the Liquid Welfare obtained in the worst equilibrium. For pure Nash equilibria of simultaneous first price auctions, we obtain a bound of 2 on the LPoA for additive buyers. Our results easily extend to the larger class of fractionally-subadditive valuations. Next we show that the LPoA of mixed Nash equilibria for first price auctions with additive bidders is bounded by a constant. Our proofs are robust, and can be extended to achieve similar bounds for Bayesian Nash equilibria. To derive our results, we develop a new technique in which some bidders deviate (surprisingly) toward a non-optimal solution. In particular, this technique goes beyond the smoothness-based approach.

Original languageEnglish
Title of host publicationAlgorithmic Game Theory - 10th International Symposium, SAGT 2017, Proceedings
EditorsVittorio Bilo, Michele Flammini
Number of pages13
StatePublished - 2017
Event10th International Symposium on Algorithmic Game Theory, SAGT 2017 - L’Aquila, Italy
Duration: 12 Sep 201714 Sep 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10504 LNCS


Conference10th International Symposium on Algorithmic Game Theory, SAGT 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


Dive into the research topics of 'Liquid price of anarchy'. Together they form a unique fingerprint.

Cite this