0
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Some remarks on Linear-quadratic closed-loop games with many players

      Preprint
      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a sparse graph, both short-time and long-time existence of a classical solution for the Nash system set in infinitely many dimensions are addressed, as well as convergence to the solution to the respective ergodic problem as the time horizon goes to infinity; in addition, equilibria for the infinite-dimensional game are shown to provide \(\epsilon\)-Nash closed-loop equilibria for the \(N\)-player game. In a setting of generalized mean-field type (where the number of interactions is large but not necessarily symmetric), directly from the \(N\)-player Nash system estimates on the value functions are deduced on an arbitrary large time horizon, which should pave the way for a convergence result as \(N\) goes to infinity.

          Related collections

          Author and article information

          Journal
          12 January 2024
          Article
          2401.06534
          702e53dc-983c-472c-a99f-72ed2dfa82a6

          http://creativecommons.org/licenses/by/4.0/

          History
          Custom metadata
          math.OC math.AP

          Analysis,Numerical methods
          Analysis, Numerical methods

          Comments

          Comment on this article