Cooperative Differential Games with the Utility Function Switched at a Random Time Moment

This paper describes a differential game of n persons in which the utility functions of the players have a hybrid form; namely, they are changed at a random moment in time. The form of the payoff functional is simplified using integration by parts. For the cooperative scenario, the problem of time-consistency of the optimality principle chosen by the players is studied and a solution is proposed in the form of an adapted imputation procedure. A differential investment game is considered as an example.