{
  "annotation_id": "5f1d1474-78ca-46e8-87ff-24bea9fde325",
  "date_created": "2026-03-02T18:02:17.041000Z",
  "date_modified": "2026-03-02T18:02:17.041000Z",
  "file_hash": "996db7d23fcc47bc1ecfc25d7062afe2ec1bb763ac5cb4cdccf2ffd100319e65",
  "private": false,
  "record": {
    "abstract": "Examples of games between two partners with mixed strategies, calculated by\nthe use of the probability amplitude as some vector in Hilbert space are given.\nThe games are macroscopic, no microscopic quantum agent is supposed. The reason\nfor the use of the quantum formalism is in breaking of the distributivity\nproperty for the lattice of yes-no questions arising due to the special rules\nof games. The rules of the games suppose two parts: the preparation and\nmeasurement. In the first part due to use of the quantum logical\northocomplemented non-distributive lattice the partners freely choose the wave\nfunctions as descriptions of their strategies. The second part consists of\nclassical games described by Boolean sublattices of the initial non-Boolean\nlattice with same strategies which were chosen in the first part. Examples of\ngames for spin one half are given. New Nash equilibria are found for some\ncases. Heisenberg uncertainty relations without the Planck constant are written\nfor the \"spin one half game\".",
    "arxiv_id": "quant-ph/0504129",
    "authors": [
      "A. A. Grib",
      "A. Yu. Khrennikov",
      "G. N. Parfionov",
      "K. A. Starkov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1874564",
    "title": "Distributivity breaking and macroscopic quantum games",
    "url": "https://arxiv.org/abs/quant-ph/0504129"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "256934d1-b6fd-4abc-b62a-ce415b43ce0b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}