{
  "annotation_id": "42ec81f3-36c4-411e-b679-4ed9cc8a8c2e",
  "date_created": "2026-03-02T18:01:04.038000Z",
  "date_modified": "2026-03-02T18:01:04.038000Z",
  "file_hash": "58ab027097a978e9ff8ddafe443a47a016e000a2318774b24ee70d2c03725f29",
  "private": false,
  "record": {
    "abstract": "We study the mean field dynamics of a model introduced by Phan et al [Wehia,\n2005] of a polymorphic social community. The individuals may choose between\nthree strategies: either not to join the community or, in the case of joining\nit, to cooperate or to behave as a free-rider. Individuals\u0027 preferences have an\nidiosyncratic component and a social component. Cooperators bear a fixed cost\nwhereas free-riders support a cost proportional to the number of cooperators.\nWe study the dynamics of this model analytically in the mean field\napproximation for both parallel and sequential updating. As we vary one of the\nparameters while keeping the other parameters fixed, the phase diagram\nexperiences a rich class of bifurcations. Noticeably, a limit cycle is shown to\nexist in both parallel and sequential updating, under certain parameter\nsettings. A comparison of the analytical predictions with computer simulation\nis also included.",
    "arxiv_id": "physics/0511194",
    "authors": [
      "Yiping Ma",
      "Mirta B. Gordon",
      "Jean-Pierre Nadal"
    ],
    "categories": [
      "physics.soc-ph"
    ],
    "title": "Dynamics of Social Systems: Cooperation and Free-Riding",
    "url": "https://arxiv.org/abs/physics/0511194"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bca5039a-3813-40b3-b59a-dcbc522e79f2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}