Probabilistic stimulation problem (Q1342610)

The paper treats a problem of the stochastic active systems (AS) theory which is better known in the English economic literature as contract theory. A general setting of the problem is presented first with mathematical specification of the objective functions of the center and of the active elements (AE). After recognizing that there is no solution method for the general problem formulation, two models containing simplifying assumptions are presented. The essential assumption leading to the first model is that the set of admissible internal plans of the AE is finite, which leads to an averaging of the objective functions of the center and of the AE. The second model circumvents the explicit presence of random variables in the problem formulation and reduces the originally stochastic problem to a deterministic one. Finally, under one additional assumption, it is shown that the solutions provided by both models coincide with each other. Numerical computer methods for determining a solution, based on either model, are outlined.