Von Neumann–Morgernstern modified generalized Raiffa solution and its application

In this paper we would like to discuss one of the possible modifications of Raiffa's unique point solution which has applications in the analysis of social networks associated with investing in social position and creating the structures based on mutual covering of violations of the generally accepted principles. These structures are formed on the base of games of Tragedy of commons type when one player detects breaking the rules by another player. Hence the first player begins bribing the other player and simultaneously covering his back, one player is rejudiced in favour of another player. This gives a rise to social networks that significantly affect the formation of coalitions in various areas of the social system, including institutions whose mission is to protect society against violations of the generally accepted principles. We also consider an original theoretical concept. We show that this concept can be used to implement the NM-modified Raiffa's solution for $n = 3$.