Nonzero-Sum Stochastic Games and Mean-Field Games with Impulse Controls

We consider a general class of nonzero-sum N-player stochastic games with impulse controls, where players control the underlying dynamics discrete interventions. adopt veri?cation approach and provide su?cient conditions for Nash equilibria (NEs) game. then limiting situation when N goes to in?nity, that is, suitable mean-?eld game (MFG) controls. show under appropriate technical conditions, there exists unique NE solution MFG, which is an ?-NE approximation game, [Formula: see text]. As example, we analyze in detail two-player extends classical cash management problem setting. In particular, present numerical analysis cases single player, showing impact competition on player’s optimal strategy, sensitivity model parameters.