The behavior of the participants in the production process at the enterprise is modeled in cases of two-level and three-level hierarchy in the conditions of corruption, checking products for quality and punishing players in a number of cases. The formulas for the interaction of players and their winning strategies are given. A number of functions are standard formulas. The Stackelberg equilibrium was obtained programmatically for a two-level system in statics, for a three-level system in dynamics. The proposed formulation is based on the theories of G.A. Ugolnitsky and A.B. Usov. The results obtained allow us to identify shortcomings in a number of enterprises, as well as in theory, and continue its development.
Keywords: analytic-geometric analysis, simulation modeling, Stackelberg equilibrium, hierarchical system, game-theoretic modeling, corruption in organizations
An application of the method of qualitatively representative scenarios of the simulation modeling to the solution of the optimal control problems in marketing is described. The idea of the method is the following. We can reduce the enumeration of very big or even infinite number of of scenarios to the very small number of them and receive a qualitatively acceptable picture of the forecasting behavior of the modeling dynamic system. The conditions of verification of the correctness of such reduction are presented. The qualitatively representative scenarios of the marketing impact on the target auduience are proposed for different control problems.
Keywords: directed graphs, differential games, dynamic control models, marketing research, social networks
A model of impact in a social network is a weighted directed graph. Its vertices correspond to the members of a social group, and its arcs describe their mutual impact. A real value (an opinion of the group's member) as a function of time is ascribed to each vertex, and a real number (weight) is ascribed to each arc (a degree of impact of one member of the group to another or, what is the same, a degree of confidence of one member of the group to another). All strong subgroups (non-degenerated strong components of the digraph) develop their final opinions which depend only to the initial opinions of their members. The final opinions of other members of the group are linear convolutions of the final opininions of all strong subgroups. A number of indices is used for the additional quantitative characteristics of the social group. From the marketing point of view, the solution of the analysis problems provides a segmentation of the target audience for the determination of the most appropriate objects of marketing impact (members of the strong subgroups).
Keywords: directed graphs, differential games, dynamic control models, marketing research, social networks
A model of impact in a social network is a weighted directed graph. Its vertices correspond to the members of a social group, and its arcs describe their mutual impact. A real value (an opinion of the group's member) as a function of time is ascribed to each vertex, and a real number (weight) is ascribed to each arc (a degree of impact of one member of the group to another or, what is the same, a degree of confidence of one member of the group to another). All strong subgroups (non-degenerated strong components of the digraph) develop their final opinions which depend only to the initial opinions of their members. The final opinions of other members of the group are linear convolutions of the final opininions of all strong subgroups. A number of indices is used for the additional quantitative characteristics of the social group. From the marketing point of view, the solution of the analysis problems provides a segmentation of the target audience for the determination of the most appropriate objects of marketing impact (members of the strong subgroups).
Keywords: directed graphs, differential games, dynamic control models, marketing research, social networks
A base model of impact in a social network is a weighted directed graph. Its vertices correspond to the members of a social group, and its arcs describe their mutual impact. A real value (an opinion of the group's member) as a function of time is ascribed to each vertex, and a real number (weight) is ascribed to each arc (a degree of impact of one member of the group to another or, what is the same, a degree of confidence of one member of the group to another). All strong subgroups (non-degenerated strong components of the digraph) develop their final opinions which depend only to the initial opinions of their members. The final opinions of other members of the group are linear convolutions of the final opininions of all strong subgroups. The most interesting question for applications arises when one or several decision makers are not satisfied by the received final opinions. To formalize such situation the base model is extended by an introduction of a set of the impact agents which can exert influence to the basic agents. The impact agents may change the initial opinions of the basic agents or the factors of their interaction. This leads to the optimal control problems or dynamic games on networks. The respective setups and their marketing interpretation are presented in the paper.
Keywords: directed graphs, differential games, dynamic control models, marketing research, social networks