Allocation of an indivisible resource: Optimal control and prices.

Under study is a dynamical system of economics with discrete time whose states at each moment correspond to nonnegative integer points of a two-dimensional vector space. There are two types of products and two facilities each of which can change the state of the system by random integer vectors with different collections of probabilities. By a control we understand the choice at each moment of time of one available collection of probabilities. The goal of control is to minimize the probability of leaving the positive quadrant. The question is considered of the existence of some prices that agree with an optimal control. [ABSTRACT FROM AUTHOR]