dorsal/arxiv
View SchemaPhase Transition in Evolutionary Games
| Authors | Zhen Cao, Rudolph C. Hwa |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9509041 |
| URL | https://arxiv.org/abs/nucl-th/9509041 |
| DOI | 10.1142/S0217751X99000786 |
| Journal | Int.J.Mod.Phys. A14 (1999) 1551-1560 |
Abstract
The evolution of cooperative behaviour is studied in the deterministic version of the Prisoners' Dilemma on a two-dimensional lattice. The payoff parameter is set at the critical region $1.8 < b < 2.0$ , where clusters of cooperators are formed in all spatial sizes. Using the factorial moments developed in particle and nuclear physics for the study of phase transition, the distribution of cooperators is studied as a function of the bin size covering varying numbers of lattice cells. From the scaling behaviour of the moments a scaling exponent is determined and is found to lie in the range where phase transitions are known to take place in physical systems. It is therefore inferred that when the payoff parameter is increased through the critical region the biological system of cooperators undergoes a phase transition to defectors. The universality of the critical behaviour is thus extended to include also this particular model of evolution dynamics.
{
"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
}