Linear-Quadratic $N$-person and Mean-Field Games: Infinite Horizon Games with Discounted Cost and Singular Limits

Autor:	Priuli, Fabio S.
Rok vydání:	2014
Předmět:	Mathematics - Analysis of PDEs Mathematics - Optimization and Control 49N70 49N10 49L25 91A23
Druh dokumentu:	Working Paper
Popis:	We consider stochastic differential games with $N$ nearly identical players, linear-Gaussian dynamics, and infinite horizon discounted quadratic cost. Admissible controls are feedbacks for which the system is ergodic. We first study the existence of affine Nash equilibria by means of an associated system of $N$ Hamilton-Jacobi-Bellman and $N$ Kolmogorov-Fokker-Planck partial differential equations, proving that for small discount factors quadratic-Gaussian solutions exist and are unique. Then, we prove the convergence of such solutions to the unique quadratic-Gaussian solution of the pair of Mean Field equations. We also discuss some singular limits, such as vanishing noise, cheap control and vanishing discount. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1403.4090 Zobrazit plný text záznamu View this record from Arxiv