{
  "annotation_id": "ffea3057-6fad-4ec1-ab80-de063505e009",
  "date_created": "2026-03-02T18:00:14.759000Z",
  "date_modified": "2026-03-02T18:00:14.759000Z",
  "file_hash": "a03ec9c268fd308919e6b55303e7cca0d6ae4d4a334b7efbe3d563df566f1164",
  "private": false,
  "record": {
    "abstract": "The evolution of cooperative behaviour is studied in the deterministic\nversion of the Prisoners\u0027 Dilemma on a two-dimensional lattice. The payoff\nparameter is set at the critical region $1.8 \u003c b \u003c 2.0$ , where clusters of\ncooperators are formed in all spatial sizes. Using the factorial moments\ndeveloped in particle and nuclear physics for the study of phase transition,\nthe distribution of cooperators is studied as a function of the bin size\ncovering varying numbers of lattice cells. From the scaling behaviour of the\nmoments a scaling exponent is determined and is found to lie in the range where\nphase transitions are known to take place in physical systems. It is therefore\ninferred that when the payoff parameter is increased through the critical\nregion the biological system of cooperators undergoes a phase transition to\ndefectors. The universality of the critical behaviour is thus extended to\ninclude also this particular model of evolution dynamics.",
    "arxiv_id": "nucl-th/9509041",
    "authors": [
      "Zhen Cao",
      "Rudolph C. Hwa"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.1142/S0217751X99000786",
    "journal_ref": "Int.J.Mod.Phys. A14 (1999) 1551-1560",
    "title": "Phase Transition in Evolutionary Games",
    "url": "https://arxiv.org/abs/nucl-th/9509041"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e6c67a2e-0b7e-4683-a262-4957a2577193",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}