{
  "id": "2303.15386",
  "version": "v1",
  "published": "2023-03-27T16:59:36.000Z",
  "updated": "2023-03-27T16:59:36.000Z",
  "title": "Robustness of Dynamics in Games: A Contraction Mapping Decomposition Approach",
  "authors": [
    "Sina Arefizadeh",
    "Sadegh Arefizadeh",
    "S. Rasoul Etesami",
    "Sadegh Bolouki"
  ],
  "categories": [
    "cs.GT"
  ],
  "abstract": "A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the asymptotic behavior of a given dynamic in a designated game. Although there is a large body literature on developing convergent dynamics to the Nash equilibrium (NE) of a game, in general, the asymptotic behavior of an underlying dynamic may not be even close to a NE. In this paper, we initiate a new direction towards game dynamics by studying the fundamental properties of the map of dynamics in games. To this aim, we first decompose the map of a given dynamic into contractive and non-contractive parts and then explore the asymptotic behavior of those dynamics using the proximity of such decomposition to contraction mappings. In particular, we analyze the non-contractive behavior for better/best response dynamics in discrete-action space sequential/repeated games and show that the non-contractive part of those dynamics is well-behaved in a certain sense. That allows us to estimate the asymptotic behavior of such dynamics using a neighborhood around the fixed point of their contractive part proxy. Finally, we demonstrate the practicality of our framework via an example from duopoly Cournot games.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-27T16:59:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "contraction mapping decomposition approach",
      "asymptotic behavior",
      "robustness",
      "better/best response dynamics",
      "discrete-action space sequential/repeated games"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}