# A Unifying Approximate Potential for Weighted Congestion Games

@inproceedings{Giannakopoulos2020AUA,
title={A Unifying Approximate Potential for Weighted Congestion Games},
author={Yiannis Giannakopoulos and Diogo Poças},
booktitle={SAGT},
year={2020}
}
• Published in SAGT 20 May 2020
• Computer Science
We provide a unifying, black-box tool for establishing existence of approximate equilibria in weighted congestion games and, at the same time, bounding their Price of Stability. Our framework can handle resources with general costs--including, in particular, decreasing ones--and is formulated in terms of a set of parameters which are determined via elementary analytic properties of the cost functions. We demonstrate the power of our tool by applying it to recover the recent result of…
1 Citations
Existence and Complexity of Approximate Equilibria in Weighted Congestion Games
• Economics
ICALP
• 2020
It is shown that deciding whether a weighted congestion game has an $\tilde{O}(\sqrt{d})$-PNE is NP-complete, and a black-box gap-introducing method of combining such nonexistence results with a specific circuit gadget is provided, in order to derive NP-completeness of the decision version of the problem.

## References

SHOWING 1-10 OF 42 REFERENCES
Existence and Complexity of Approximate Equilibria in Weighted Congestion Games
• Economics
ICALP
• 2020
It is shown that deciding whether a weighted congestion game has an $\tilde{O}(\sqrt{d})$-PNE is NP-complete, and a black-box gap-introducing method of combining such nonexistence results with a specific circuit gadget is provided, in order to derive NP-completeness of the decision version of the problem.
On the Performance of Approximate Equilibria in Congestion Games
• Economics
Algorithmica
• 2010
This work studies the performance of approximate Nash equilibria for congestion games with polynomial latency functions and provides a unified approach which reveals the common threads of the atomic and non-atomic price of anarchy results.
Efficient Computation of Approximate Pure Nash Equilibria in Congestion Games
• Computer Science, Economics
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
• 2011
This work presents a surprisingly simple polynomial-time algorithm that computes $O(1)$-approximate Nash equilibria in non-symmetric congestion games and proves that, for congestion games that deviate from the mild assumptions, computing $\rho$- Approximate Equilibria is {\sf PLS}-complete for any polynomially-time computable $rho$.
On approximate pure Nash equilibria in weighted congestion games with polynomial latencies
• Economics
ICALP
• 2019
Using a simple potential function argument, it is shown that a d-approximate pure Nash equilibrium of cost at most $(d+1)/(d+\delta)$ times the cost of an optimal state always exists, for $\delta\in [0,1]$.
Algorithms for pure Nash equilibria in weighted congestion games
• Computer Science
ACM J. Exp. Algorithmics
• 2006
A by-product of this research is the discovery of a weighted potential function when link delays are exponential to their loads, which asserts the existence of pure Nash equilibria for these delay functions and extends the result of Fotakis et al.
Improved Lower Bounds on the Price of Stability of Undirected Network Design Games
• Computer Science
Theory of Computing Systems
• 2012
The psychological barrier of 2 is broken by showing that the price of stability of undirected network design games is at least 348/155≈2.245, and the lower bounds are improved as follows.
Hermite and convexity
• Mathematics
• 1985