In this talk we consider a stochastic di?fferential game where each player can control the di?ffusion intensity of an individual dynamic state process, and the players whose states at a deterministic ?finite time horizon are among the best alpha of all states receive a ?fixed prize. Within the mean-?field limit version of the game we compute an explicit equilibrium, a threshold strategy that consists in choosing the maximal fluctuation intensity when the state is below a given threshold, and the minimal intensity else. We show that for large n the symmetric n-tuple of the threshold strategy provides an approximate Nash-equilibrium of the n-player game. Finally, we compare the approximate equilibrium for large games with the equilibrium of the two player case.
The talk is based on joint work with Nabil Kazi-Tani, Julian Wendt and Chao Zhou.