{
  "id": "1703.02088",
  "version": "v1",
  "published": "2017-03-06T19:58:20.000Z",
  "updated": "2017-03-06T19:58:20.000Z",
  "title": "The Naming Game on the complete graph",
  "authors": [
    "Eric Foxall"
  ],
  "comment": "34 pages, no figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a model of language development, known as the naming game, in which agents invent, share and then select descriptive words for a single object, in such a way as to promote local consensus. When formulated on a finite and connected graph, a global consensus eventually emerges in which all agents use a common unique word. Previous numerical studies of the model on the complete graph with $n$ agents suggest that when no words initially exist, the time to consensus is of order $n^{1/2}$, assuming each agent speaks at a constant rate. We show rigorously that the time to consensus is at least $n^{1/2-o(1)}$, and that it is at most constant times $\\log n$ when only two words remain. In order to do so we develop sample path estimates for quasi-left continuous semimartingales with bounded jumps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-06T19:58:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G99"
    ],
    "keywords": [
      "complete graph",
      "naming game",
      "sample path estimates",
      "common unique word",
      "promote local consensus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}