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Stochastic Differential Games with a Major Player and a Large Number of Minor Players

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We consider stochastic differential games involving a major player and $N$ minor players. The nonlinear payoff functional associated with the controlled state processes of the $N+1$ players is defined by a controlled backward stochastic differential equation. Our objective is to the study of the limit behavior of the Nash equilibrium payoffs and the associated optimal controls as $N$ tends to infinity, as well as to describe the limit game and to describe the associated SPDE of McKean-Vlasov type. Our work has been strongly motivated by earlier works on mean-field games by J.-M.Lasry and P.-L.Lions (2007) as well as by recent works on large-population stochastic linear-quadratic games involving a major player by M.Huang (2008) and F.Hu (2009).

My talk is based on common work with Juan Li and Shige Peng from the Shandong University in Weihai and Jinan (P.R.China), respectively.

This talk is part of the Isaac Newton Institute Seminar Series series.

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