Mathematical Approach to Many-Staged Distribution of Social Significant Resource if there is a Rating of Consumers

Abstract

It is given a description of a mathematical approach to distribution of limited resource of social economic contents between people groups, which are under different conditions, in  the case when it takes place during several stages separated by time intervals. This approach is based on (worked out earlier) the mathematical algorithm of a single distribution of limited  social significant resource in justice principles in the presence of two-level scale: a rating of consumers (people groups) and   a numerical scale  reflecting size of their needs. It is given a numerical realization of this algorithm as an example of the solution of the management problem by collective investment of long-term construction of an immovable object, when investors pay money in a building firm by stages. Moreover, in connection with money contents of the resource it is presented a  mathematical model of “rational” interaction of investors both inside every group, and between groups for the sole of time investment of the building firm at every stage of financing. It is adduced a numerical illustration of this model at the same example.