Decision Making Behaviours Represented in a Formal System

Following the definitions of concepts of the linear algebra in a finite manner, two natural decision-making behaviours are constructively represented in a formal axiomatic system assuming the existence of the rational numbers and their arithmetics. Their capabilities of the optimal planning for the global organizations under the decentralized administrations are shown to be provable in the formal system. I. e., the optimal planning is shown to be computable on the Turing machine. In model 1 each branch is rather independent and the headquarters control the branches through the appropriate information flow. Model 2 has no headquarters and the natural bargaining process between the branches yields the optimal plan for the global organization.