Hierarchical games with feedback on the assumption of a lower-level player's benevolence

A new optimality principle is proposed that generalizes the Stackelberg equilibrium principle. Its connection with the classical definition is investigated. The technique of working with the new definition is discussed. As an example, solutions are found in two hierarchical games with feedback.

CONSTRUCTION OF COMPLEX SCHEDULES FOR EXECUTION OF TASK PACKAGES AT FORMING SETS IN SPECIFIED DIRECTIVE TERMS

The current state with the solution of the problem complex planning of the execution of task packets in multistage system is characterized by the absence of universal methods of forming decisions on the composition of packets, the presence of restrictions on the dimension of the problem and the impossibility of guaranteed obtaining effective solutions for various values of its input parameters, as well the impossibility of registration the condition of the formation of sets from the results. The solution of the task of planning the execution of task packets in multistage systems with the formation of sets of results within the specified deadlines has been realized of authors in article. To solve the planning problem, the generalized function of the system was decomposed into a set of hierarchically interrelated subfunctions. The use of decomposition made it possible to use a hierarchical approach for planning the execution of task packets in multistage systems, which involves defining solutions based on the composition of packets at the top level of the hierarchy and scheduling the execution of packages at the bottom level of the hierarchy. The theory of hierarchical games is used to optimize solutions for the compositions of task packets and schedules for their execution is built, which is a system of criteria at the decision-making levels. Evaluation of the effectiveness of decisions by the composition of packets at the top level of the hierarchy is ensured by the distribution of the results of task execution by packets in accordance with the formed schedule. To evaluate the effectiveness of decisions on the composition of packets, method for ordering the identifiers of the types of sets with registration of the deadlines and a method for distributing the results of the tasks performed by packets has been formulated, which calculates the moments of completion of the formation of sets and delays with their formation relative to the specified deadlines. The studies of planning the process of the executing task packages in multistage systems have been carried out, provided that the sets are formed within specified deadlines. On their basis, conclusions, regarding the dependence of the planning efficiency from the input parameters of the problem, were formulated.

Hierarchy and the size of a firm

In this note, we apply weighted hierarchical games of cooperative game theory to the problem of optimal firm size of the firm. In particular, we analyze the influence of production technology on the size of the firm. Our note enhances previous approaches using a permission structure with equally strong relationships between predecessor and direct successors.