Existence and complexity of approximate equilibria in weighted congestion games

Christodoulou G, Gairing M, Giannakopoulos Y, Poças D, Waldmann C (2020)

Publication Type: Conference contribution, Original article

Publication year: 2020

Journal

LIPIcs : Leibniz International Proceedings in Informatics Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik

Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Book Volume: 168

Pages Range: 32:1--32:18

Conference Proceedings Title: Proceedings of the 47th International Colloquium on Automata, Languages, and Programming (ICALP)

ISBN: 9783959771382

DOI: 10.4230/LIPIcs.ICALP.2020.32

Open Access Link: https://drops.dagstuhl.de/opus/volltexte/2020/12439/

Abstract

We study the existence of approximate pure Nash equilibria (α-PNE) in weighted atomic congestion games with polynomial cost functions of maximum degree d. Previously it was known that d-approximate equilibria always exist, while nonexistence was established only for small constants, namely for 1.153-PNE. We improve significantly upon this gap, proving that such games in general do not have Θ~(√d)-approximate PNE, which provides the first super-constant lower bound. Furthermore, we provide a black-box gap-introducing method of combining such nonexistence results with a specific circuit gadget, in order to derive NP-completeness of the decision version of the problem. In particular, deploying this technique we are able to show that deciding whether a weighted congestion game has an Õ(√d)-PNE is NP-complete. Previous hardness results were known only for the special case of exact equilibria and arbitrary cost functions. The circuit gadget is of independent interest and it allows us to also prove hardness for a variety of problems related to the complexity of PNE in congestion games. For example, we demonstrate that the question of existence of α-PNE in which a certain set of players plays a specific strategy profile is NP-hard for any α < 3d/2, even for unweighted congestion games. Finally, we study the existence of approximate equilibria in weighted congestion games with general (nondecreasing) costs, as a function of the number of players n. We show that n-PNE always exist, matched by an almost tight nonexistence bound of Θ~(n) which we can again transform into an NP-completeness proof for the decision problem.

Authors with CRIS profile

Ioannis Giannakopoulos

Involved external institutions

Technische Universität München (TUM) DE Germany (DE) The University of Liverpool GB United Kingdom (GB)

How to cite

APA:

Christodoulou, G., Gairing, M., Giannakopoulos, Y., Poças, D., & Waldmann, C. (2020). Existence and complexity of approximate equilibria in weighted congestion games. In Artur Czumaj, Anuj Dawar, Emanuela Merelli (Eds.), Proceedings of the 47th International Colloquium on Automata, Languages, and Programming (ICALP) (pp. 32:1--32:18). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.

MLA:

Christodoulou, George, et al. "Existence and complexity of approximate equilibria in weighted congestion games." Proceedings of the 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 Ed. Artur Czumaj, Anuj Dawar, Emanuela Merelli, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2020. 32:1--32:18.

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