{
  "id": "2304.02998",
  "version": "v1",
  "published": "2023-04-06T11:13:56.000Z",
  "updated": "2023-04-06T11:13:56.000Z",
  "title": "Multiple-Population Discrete-Time Mean Field Games with Discounted and Total Payoffs: The Existence of Equilibria",
  "authors": [
    "Piotr Więcek"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In the paper we present a model of discrete-time mean-field game with several populations of players. Mean-field games with multiple populations of the players have only been studied in the literature in the continuous-time setting. The main results of this article are the first stationary and Markov mean-field equilibrium existence theorems for discrete-time mean-field games of this type. We consider two payoff criteria: discounted payoff and total payoff. The results are provided under some rather general assumptions on one-step reward functions and individual transition kernels of the players. In addition, the results for total payoff case, when applied to a single population, extend the theory of mean-field games also by relaxing some strong assumptions used in the existing literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-06T11:13:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A15",
      "91A13",
      "91A10"
    ],
    "keywords": [
      "multiple-population discrete-time mean field games",
      "total payoff",
      "mean-field equilibrium existence theorems",
      "discrete-time mean-field game"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}