---
_id: '271'
abstract:
- lang: eng
text: In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists
of various demands on different resources. The player's utility is at most the
sum of these demands, provided they are fully satisfied. Every resource has a
limited capacity and if it is exceeded by the total demand, it has to be split
between the players. Since these games generally do not have pure Nash equilibria,
we consider approximate pure Nash equilibria, in which no player can improve her
utility by more than some fixed factor $\alpha$ through unilateral strategy changes.
There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits
the demand of each player on a specific resource) such that $\alpha$-approximate
pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for
$\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold
$\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard.
We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$.
For a restricted version of the game, where demands of players only differ slightly
from each other (e.g. symmetric games), we show that approximate Nash equilibria
can be reached (and thus also be computed) in polynomial time using the best-response
dynamic. Finally, we show that a broader class of utility-maximization games (which
includes BAGs) converges quickly towards states whose social welfare is close
to the optimum.
author:
- first_name: Maximilian
full_name: Drees, Maximilian
last_name: Drees
- first_name: Matthias
full_name: Feldotto, Matthias
id: '14052'
last_name: Feldotto
orcid: 0000-0003-1348-6516
- first_name: Sören
full_name: Riechers, Sören
last_name: Riechers
- first_name: Alexander
full_name: Skopalik, Alexander
id: '40384'
last_name: Skopalik
citation:
ama: 'Drees M, Feldotto M, Riechers S, Skopalik A. On Existence and Properties of
Approximate Pure Nash Equilibria in Bandwidth Allocation Games. In: *Proceedings
of the 8th International Symposium on Algorithmic Game Theory (SAGT)*. Lecture
Notes in Computer Science. ; 2015:178-189. doi:10.1007/978-3-662-48433-3_14'
apa: Drees, M., Feldotto, M., Riechers, S., & Skopalik, A. (2015). On Existence
and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games.
In *Proceedings of the 8th International Symposium on Algorithmic Game Theory
(SAGT)* (pp. 178–189). https://doi.org/10.1007/978-3-662-48433-3_14
bibtex: '@inproceedings{Drees_Feldotto_Riechers_Skopalik_2015, series={Lecture Notes
in Computer Science}, title={On Existence and Properties of Approximate Pure Nash
Equilibria in Bandwidth Allocation Games}, DOI={10.1007/978-3-662-48433-3_14},
booktitle={Proceedings of the 8th International Symposium on Algorithmic Game
Theory (SAGT)}, author={Drees, Maximilian and Feldotto, Matthias and Riechers,
Sören and Skopalik, Alexander}, year={2015}, pages={178–189}, collection={Lecture
Notes in Computer Science} }'
chicago: Drees, Maximilian, Matthias Feldotto, Sören Riechers, and Alexander Skopalik.
“On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth
Allocation Games.” In *Proceedings of the 8th International Symposium on Algorithmic
Game Theory (SAGT)*, 178–89. Lecture Notes in Computer Science, 2015. https://doi.org/10.1007/978-3-662-48433-3_14.
ieee: M. Drees, M. Feldotto, S. Riechers, and A. Skopalik, “On Existence and Properties
of Approximate Pure Nash Equilibria in Bandwidth Allocation Games,” in *Proceedings
of the 8th International Symposium on Algorithmic Game Theory (SAGT)*, 2015,
pp. 178–189.
mla: Drees, Maximilian, et al. “On Existence and Properties of Approximate Pure
Nash Equilibria in Bandwidth Allocation Games.” *Proceedings of the 8th International
Symposium on Algorithmic Game Theory (SAGT)*, 2015, pp. 178–89, doi:10.1007/978-3-662-48433-3_14.
short: 'M. Drees, M. Feldotto, S. Riechers, A. Skopalik, in: Proceedings of the
8th International Symposium on Algorithmic Game Theory (SAGT), 2015, pp. 178–189.'
date_created: 2017-10-17T12:41:45Z
date_updated: 2022-01-06T06:57:34Z
ddc:
- '040'
department:
- _id: '63'
- _id: '541'
doi: 10.1007/978-3-662-48433-3_14
external_id:
arxiv:
- '1507.02908'
file:
- access_level: closed
content_type: application/pdf
creator: florida
date_created: 2018-03-21T09:29:34Z
date_updated: 2018-03-21T09:29:34Z
file_id: '1475'
file_name: 271-chp_3A10.1007_2F978-3-662-48433-3_14.pdf
file_size: 256718
relation: main_file
success: 1
file_date_updated: 2018-03-21T09:29:34Z
has_accepted_license: '1'
page: 178-189
project:
- _id: '1'
name: SFB 901
- _id: '7'
name: SFB 901 - Subprojekt A3
- _id: '16'
name: SFB 901 - Subproject C4
- _id: '2'
name: SFB 901 - Project Area A
- _id: '4'
name: SFB 901 - Project Area C
publication: Proceedings of the 8th International Symposium on Algorithmic Game Theory
(SAGT)
series_title: Lecture Notes in Computer Science
status: public
title: On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth
Allocation Games
type: conference
user_id: '14052'
year: '2015'
...