{"paper":{"title":"Pure Nash Equilibria in Graphical Games of Bounded Width Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.GT"],"primary_cat":"cs.DS","authors_text":"Michael Lampis, Yiren Lu","submitted_at":"2026-07-08T16:43:19Z","abstract_excerpt":"We revisit the complexity of deciding whether a graphical game admits a pure Nash equilibrium (PNE) parameterized by standard measures of the input graph, such as treewidth. The natural dynamic programming algorithm for this problem has parameter dependence $\\alpha^{(\\Delta+1)\\text{tw}}$ where $\\alpha$ is the maximum number of strategies available to each player, each player's utility depends on at most $\\Delta$ other players, and the input graph has width $\\text{tw}$. Our first contribution is to point out that an algorithm by Thomas and van Leeuwen [Algorithmica 2015] claiming to improve thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07627","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.07627/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}