--- res: bibo_abstract: - We revisit the simple class of weighted congestion games on parallel links [10], where each player has a non-negative weight and her cost on the link she chooses is the sum of the weights of all players choosing the link. We extend this class to mix-weighted congestion games on parallel links, where weights may as well be negative. For the resulting simple class, we study the complexity of deciding the existence of a pure equilibrium, where no player could unilaterally improve her cost by switching to another link.We show that even for a singlenegative weight, this decision problem is strongly NP-complete when the number of links is part of the input; the problem is NP-complete already for two links. When the number of links is a fixed constant, we show, through a pseudopolynomial, dynamic programming algorithm, that the problem is not strongly NP-complete unless P = NP; the algorithm works for any number of negative weights.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Burkhard foaf_name: Monien, Burkhard foaf_surname: Monien - foaf_Person: foaf_givenName: Marios foaf_name: Mavronicolas, Marios foaf_surname: Mavronicolas bibo_doi: 10.1016/j.ipl.2015.07.012 bibo_issue: '12' bibo_volume: 115 dct_date: 2015^xs_gYear dct_language: eng dct_publisher: Elsevier@ dct_title: The complexity of pure equilibria in mix-weighted congestion games on parallel links@ ...