{
  "id": "cond-mat/0004196",
  "version": "v1",
  "published": "2000-04-12T13:10:06.000Z",
  "updated": "2000-04-12T13:10:06.000Z",
  "title": "Relevance of memory in Minority Games",
  "authors": [
    "Damien Challet",
    "Matteo Marsili"
  ],
  "comment": "10 pages, 9 figures, using RevTex",
  "doi": "10.1103/PhysRevE.62.1862",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "By considering diffusion on De Bruijn graphs, we study in details the dynamics of the histories in the Minority Game, a model of competition between adaptative agents. Such graphs describe the structure of temporal evolution of $M$ bits strings, each node standing for a given string, i.e. a history in the Minority Game. We show that the frequency of visit of each history is not given by $1/2^M$ in the limit of large $M$ when the transition probabilities are biased. Consequently all quantities of the model do significantly depend on whether the histories are real, or uniformly and randomly sampled. We expose a self-consistent theory of the case of real histories, which turns out to be in very good agreement with numerical simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-04-12T13:10:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minority game",
      "bits strings",
      "real histories",
      "bruijn graphs",
      "transition probabilities"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}