{
  "id": "2404.10428",
  "version": "v1",
  "published": "2024-04-16T09:46:24.000Z",
  "updated": "2024-04-16T09:46:24.000Z",
  "title": "Zero-Sum Games for Volterra Integral Equations and Viscosity Solutions of Path-Dependent Hamilton-Jacobi Equations",
  "authors": [
    "Mikhail I. Gomoyunov"
  ],
  "categories": [
    "math.OC",
    "math.DS"
  ],
  "abstract": "We consider a game, in which the dynamics is described by a non-linear Volterra integral equation of Hammerstein type with a weakly-singular kernel and the goals of the first and second players are, respectively, to minimize and maximize a given cost functional. We propose a way of how the dynamic programming principle can be formalized and the theory of generalized (viscosity) solutions of path-dependent Hamilton--Jacobi equations can be developed in order to prove the existence of the game value, obtain a characterization of the value functional, and construct players' optimal feedback strategies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-16T09:46:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "45D05",
      "49L20",
      "49L25",
      "49N70"
    ],
    "keywords": [
      "path-dependent hamilton-jacobi equations",
      "viscosity solutions",
      "zero-sum games",
      "non-linear volterra integral equation",
      "optimal feedback strategies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}