The paper disproves a prior FPT algorithm for PNE in graphical games of bounded treewidth, proves W[1]-hardness, and gives improved algorithms with matching pw-SETH lower bounds for pathwidth and cutwidth.
The complexity of computational problems about nash equilibria in symmetric win-lose games
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Pure Nash Equilibria in Graphical Games of Bounded Width Revisited
The paper disproves a prior FPT algorithm for PNE in graphical games of bounded treewidth, proves W[1]-hardness, and gives improved algorithms with matching pw-SETH lower bounds for pathwidth and cutwidth.