{
  "id": "1805.03849",
  "version": "v1",
  "published": "2018-05-10T06:53:54.000Z",
  "updated": "2018-05-10T06:53:54.000Z",
  "title": "On Arbitrarily Long Periodic Orbits of Evolutionary Games on Graphs",
  "authors": [
    "Jeremias Epperlein",
    "Vladimír Švígler"
  ],
  "categories": [
    "math.DS",
    "math.CO"
  ],
  "abstract": "A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters describing social-dilemma games. We construct graphs and corresponding initial conditions whose trajectories are periodic with an arbitrary minimal period length. We also examine a periodic behavior of evolutionary games on graphs with the underlying graph being an acyclic (tree) graph. Astonishingly, even this acyclic structure allows for arbitrary long periodic behavior.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-10T06:53:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A22",
      "05C57",
      "91A43",
      "37N40"
    ],
    "keywords": [
      "arbitrarily long periodic orbits",
      "evolutionary games",
      "arbitrary long periodic behavior",
      "arbitrary minimal period length",
      "display periodic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}