A rank-based mean field game in the strong formulation. (English) Zbl 1415.91050

Bayraktar, Erhan; Zhang, Yuchong

Electron. Commun. Probab. 21, Paper No. 72, 12 p. (2016).

Summary: We discuss a natural game of competition and solve the corresponding mean field game with common noise when agents’ rewards are rank-dependent. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence.

MSC:

91A23	Differential games (aspects of game theory)
91A06	\(n\)-person games, \(n>2\)
91A15	Stochastic games, stochastic differential games
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

mean field games; stochastic differential equations; competition; common noise; rank-dependent interaction; non-local interaction; strong formulation