Limiting Behavior of LQ Deterministic Infinite Horizon Nash Games with Symmetric Players as the Number of Players goes to Infinity

Abstract

A Linear Quadratic Deterministic Continuous Time Game with many symmetric players is considered and the Linear Feedback Nash strategies are studied as the number of players goes to infinity. We show that under some conditions the limit of the solutions exists and can be used to approximate the case with a finite but large number of players. It is shown that in the limit each player acts as if he were faced with one player only, who represents the average behavior of the others.

References in corpus (1)

• Linear-Quadratic Mean Field Games

Cited by in corpus (3)

• Linear Quadratic Mean Field Games -- Part I: The Asymptotic Solvability Problem
• Linear quadratic mean field games: Asymptotic solvability and relation to the fixed point approach
• Linear quadratic mean field games with a major player: The multi-scale approach