An Alternative Approach to Mean Field Game with Major and Minor Players, and Applications to Herders Impacts

By René A. Carmona, Peiqi Wang. 2016

47 citations recorded by the source corpus.

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean–Vlasov dynamics in some of the players’ optimization problems. We apply this approach to linear quadratic models for which we recover the existing solutions for open loop equilibria, and we show that we can also provide solutions for closed loop versions of the game. Finally, we implement numerically our theoretical results on a simple model of flocking.

Subfields: Aerospace Engineering, Computer Networks and Communications, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/030fdc76354b4f8e85c93eabc0cce5d569cde921

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In Modeling and Simulation

1. Pierre Cardaliaguet
2. Alessio Porretta

Citations in the corpus

• Splitting methods and short time existence for the master equations in mean field games (2020, background): “Mean field games with a major player have been first discussed by Huang in [20] and several notions of equilibria, in different contexts, have been proposed in the literature since then: see [5, 6, 7, 8, 11, 13, 14, 15, 26].”