Cooperation in a conflict of $n$ persons under uncertainty

The paper considers a model of a conflict system with $N$ active participants with their own interests when exposed to an uncertain factor. At the same time, decision-makers do not have any statistical information about the possible implementation of an uncertain factor i.e. they only know the many possible realizations of this factor – uncertainties. Under the assumption that the participants of to the conflict can coordinate their actions in the decision-making process the model is formalized as a cooperative $N$-person game without side payments and under uncertainty. In this paper, we introduce a new principle of coalitional equilibration (CE). The integration of individual and collective rationality (from theory of cooperative games without side payments) and this principle allows us to formalize the corresponding concept of CE for a conflict of $N$ persons under uncertainty. At the same time, uncertainty is taken into account along with using the concept of the “analogue of maximin” proposed earlier in the our works and the “strong guarantees” constracted on its basis. Next, we establish sufficient conditions for existence of coalitional equilibrium, which are reduced to saddle point design for the Germeier convolution of guaranteed payoffs. Following the above-mentioned approach of E. Borel, J. von Neumann and J. Nash, we also prove existence of coalitional equilibrium in the class of mixed strategies under standard assumptions of mathematical game theory (compact uncertainties, compact strategy sets, and continuous payoff functions). At the end of the paper, some directions or further research are given.