A new approach to cooperation in a conflict with four members

This paper introduces the concept of coalition rationality. The coalition equilibrium situation (CES) in the conflict of four persons under uncertainty is formalized by unifying the notions of individual and collective rationality (from the theory of cooperative games without side payments) and the definition of coalition rationality given in this paper. Then sufficient conditions for the existence of CES, which reduce to construction of the saddle point of Germeier convolution of payoff function guarantee, are established. Next, according to approach of E. Borel, J. von Neumann, and J. Nash, the existence of CES in mixed strategies is proved under “usual” restrictions for mathematical games theory such as compactness of sets of uncertainties and strategies of players and continuity of payoff functions. In conclusion, the article suggests possible directions for further research.