On the existence of IDP-core in cooperative differential games

In this paper we consider differential games with transferable utility and study of non-emptiness property of IDP-core presented in [7]. We apply methods of linear programming first applied in the paper [23] for analyzing non-emptiness of the Core. With described methods we construct necessary and sufficient conditions for IDP-core to be non-empty. This conditions are formalized for each time instant on which the game is defined and are imposed on a set of imputation distribution procedures (IDPs) corresponding to IDP-core.