Linear-quadratic N-person and mean-field games: Infinite Horizon Games with Discounted Cost and Singular Limits (Articolo in rivista)

Type
Label
  • Linear-quadratic N-person and mean-field games: Infinite Horizon Games with Discounted Cost and Singular Limits (Articolo in rivista) (literal)
Anno
  • 2014-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1007/s13235-014-0129-8 (literal)
Alternative label
  • Priuli, Fabio S. (2014)
    Linear-quadratic N-person and mean-field games: Infinite Horizon Games with Discounted Cost and Singular Limits
    in Dynamic games and applications (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Priuli, Fabio S. (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Istituto per le Applicazioni del Calcolo \"M. Picone\", C.N.R, Rome, Italy (literal)
Titolo
  • Linear-quadratic N-person and mean-field games: Infinite Horizon Games with Discounted Cost and Singular Limits (literal)
Abstract
  • 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 discount, vanishing noise, and cheap control. (literal)
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