Strategically supported cooperation in differential games with coalition structures

The problem of strategic stability of long-range cooperative agreements in differential games with coalition structures is investigated. We build a general theoretical framework of the cooperative differential game with a coalition structure basing on imputation distribution procedure. The notion of imputation distribution procedure is the basic ingredient in our theory. This notion may be interpreted as an instantaneous payoff of an individual at some moment which prescribes distribution of the total gain among the members of a group and yields the existence of a Nash equilibrium. Moreover, a few assumptions about deviation instant for a coalition are made concerning behavior of a group of many individuals in certain dynamic environments; thus, the time-consistent cooperative agreement can be strategically supported by an $\varepsilon$-Nash equilibrium or a strong $\varepsilon$-Nash equilibrium.