Strong Strategic Support of Cooperative Solutions in Differential Games

The problem of strategically provided cooperation in n-persons differential games with integral payoffs is considered. Based on initial differential game the new associated differential game (CD-game) is designed. In addition to the initial game it models the players actions connected with transition from the strategic form of the game to cooperative with in advance chosen principle of optimality. The model provides possibility of refusal from cooperation at any time instant $t$ for each player. As cooperative principle of optimality the core operator is considered. It is supposed that components of an imputation form the core along any admissible trajectory are absolutely continuous functions of time. In the bases of CD-game construction lies the so-called imputation distribution procedure described earlier in (Petrosjan and Zenkevich, 2009). The theorem established by authors says that if at each instant of time along the conditionally optimal (cooperative) trajectory the future payments to each coalition of players according to the imputation distribution procedure exceed the maximal guaranteed value which this coalition can achieve in CD-game, then there exist a strong Nash equilibrium in the class of recursive strategies first introduced in (Chistyakov, 1999). The proof of this theorem uses results and methods published in (Chistyakov, 1999, Chentsov, 1976).