{
  "abstract": "We study approximate Nash equilibria in nonatomic congestion games, with the goal of understanding how much the social cost can change when the equilibrium condition is relaxed. We consider $ε$-approximate Nash equilibria ($ε$-NE), in which each player uses a strategy whose cost is at most $1 + ε$ times the minimum available cost. We compare the social costs of $ε$-NE and exact Nash equilibria. This lets us quantify, for example, how much a navigation app can reduce total travel time when drivers tolerate routes slightly slower than the fastest available route. For degree-$d$ polynomial latencies in both general nonatomic congestion games and single-commodity routing games on series-parallel networks, we give tight lower and upper bounds on the relative change in social cost from an exact Nash equilibrium to any $ε$-NE, with matching instances for every $ε$. For small $ε$, the largest possible relative reduction and increase in general congestion games are both $Θ(\\sqrt{dε})$, independently of the number of resources and populations. In contrast, on series-parallel networks of depth $h$, the largest possible relative reduction is $Θ(hε)$, while the largest possible relative increase is known to be $ε$. For the classes of games we study, these results give a tight and quantitative characterization of the possible changes in social cost and establish a separation between general and series-parallel networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01234",
  "author_total": 2,
  "authors": [
    {
      "name": "Yu Cheng"
    },
    {
      "name": "Tianle Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1g7jh4r55n5bf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01234",
  "fulltext_url": null,
  "id": "1g7jh4r55n5bf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01234",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "cs.GT"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01234",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1g7jh4r55n5bf.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01234",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01234"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "How Much Can Approximate Equilibria Change the Social Cost of Selfish Routing?",
  "title_text": "How Much Can Approximate Equilibria Change the Social Cost of Selfish Routing?",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/1g7jh4r55n5bf",
  "venue": "arXiv",
  "versions": []
}