{
  "id": "1607.08748",
  "version": "v1",
  "published": "2016-07-29T09:47:05.000Z",
  "updated": "2016-07-29T09:47:05.000Z",
  "title": "Cyclic dominance in a 2-person Rock-Scissors-Paper game",
  "authors": [
    "Liliana Garrido-da-Silva",
    "Sofia B. S. D. Castro"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The Rock-Scissors-Paper game has been studied in the context of single population dynamics to account for cyclic behaviour. We use a 2-person parametrised version of this game to illustrate how cyclic behaviour is still a dominant feature of the dynamics. The cyclic behaviour is observed near a heteroclinic cycle with two nodes such that, at each node, players alternate in winning and losing. This cycle is shown to be as stable as possible for a wide range of parameter values. The parameters are related to the players' payoff when a tie occurs. This cycle is part of a heteroclinic network: there are two other cycles with two nodes and two cycles with three nodes. The cycles with two nodes exhibit some intermediate stability for a large subset of parameter space, contained in the complement of the set of stability of the first cycle. These two-node cycles represent oscillations between a tie between players and a win for only one of the players. The three-node cycles are always unstable and describe a cycle among all possible outcomes in the game, in the two possible sequences. Using some applications to price setting models, we propose what could be a starting point for the contribution of the Rock-Scissors-Paper game to the understanding of cyclic dominance in two-player games.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-29T09:47:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C37",
      "91B55",
      "91A22",
      "91A05",
      "91A10"
    ],
    "keywords": [
      "rock-scissors-paper game",
      "cyclic dominance",
      "cyclic behaviour",
      "two-node cycles represent oscillations",
      "single population dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}