Node Max-Cut and Computing Equilibria in Linear Weighted Congestion Games
Abstract
In this work, we seek a more refined understanding of the complexity of local optimum computation for Max-Cut and pure Nash equilibrium (PNE) computation for congestion games with weighted players and linear latency functions. We show that computing a PNE of linear weighted congestion games is PLS-complete either for very restricted strategy spaces, namely when player strategies are paths on a series-parallel network with a single origin and destination, or for very restricted latency functions, namely when the latency on each resource is equal to the congestion. Our results reveal a remarkable gap regarding the complexity of PNE in congestion games with weighted and unweighted players, since in case of unweighted players, a PNE can be easily computed by either a simple greedy algorithm (for series-parallel networks) or any better response dynamics (when the latency is equal to the congestion). For the latter of the results above, we need to show first that computing a local optimum of a natural restriction of Max-Cut, which we call \emph{Node-Max-Cut}, is PLS-complete. In Node-Max-Cut, the input graph is vertex-weighted and the weight of each edge is equal to the product of the weights of its endpoints. Due to the very restricted nature of Node-Max-Cut, the reduction requires a careful combination of new gadgets with ideas and techniques from previous work. We also show how to compute efficiently a -approximate equilibrium for Node-Max-Cut, if the number of different vertex weights is constant.
Cite
@article{arxiv.1911.08704,
title = {Node Max-Cut and Computing Equilibria in Linear Weighted Congestion Games},
author = {Dimitris Fotakis and Vardis Kandiros and Thanasis Lianeas and Nikos Mouzakis and Panagiotis Patsilinakos and Stratis Skoulakis},
journal= {arXiv preprint arXiv:1911.08704},
year = {2020}
}