{
  "annotation_id": "e0818590-015a-4267-a060-0100a14fee26",
  "date_created": "2026-03-02T18:01:34.969000Z",
  "date_modified": "2026-03-02T18:01:34.969000Z",
  "file_hash": "b1c41490748096fee74201070efe2b3d4e86bbed4a55b0cc990a026e495c7809",
  "private": false,
  "record": {
    "abstract": "We study the connection between the evolutionary replicator dynamics and the\nnumber of Nash equilibria in large random bi-matrix games. Using techniques of\ndisordered systems theory we compute the statistical properties of both, the\nfixed points of the dynamics and the Nash equilibria. Except for the special\ncase of zero-sum games one finds a transition as a function of the so-called\nco-operation pressure between a phase in which there is a unique stable fixed\npoint of the dynamics coinciding with a unique Nash equilibrium, and an\nunstable phase in which there are exponentially many Nash equilibria with\nstatistical properties different from the stationary state of the replicator\nequations. Our analytical results are confirmed by numerical simulations of the\nreplicator dynamics, and by explicit enumeration of Nash equilibria.",
    "arxiv_id": "q-bio/0608032",
    "authors": [
      "Tobias Galla"
    ],
    "categories": [
      "q-bio.PE",
      "cond-mat.dis-nn",
      "cond-mat.stat-mech"
    ],
    "doi": "10.1209/0295-5075/78/20005",
    "title": "Two-population replicator dynamics and number of Nash equilibria in   random matrix games",
    "url": "https://arxiv.org/abs/q-bio/0608032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c477e8af-2344-480c-924f-cb1777c6960c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}