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

Fabio Priuli ()

Dynamic Games and Applications, 2015, vol. 5, issue 3, 397-419

Abstract: We consider stochastic differential games with $$N$$ 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 $$N$$ N Hamilton–Jacobi–Bellman and $$N$$ 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. Copyright Springer Science+Business Media New York 2015

Keywords: Linear-quadratic differential games; Nash equilibria; Mean field games (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13235-014-0129-8

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