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}
}
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
TLDR
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.

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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.
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