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The discrete- and continuous-time network models of opinions control and resource allocation in marketing are considered. Three cases of interaction of economic agents are studied: independent behavior, cooperation, and hierarchical control by the resource-owning Principal. The corresponding dynamic games are analytically solved. The agents' payoffs in these cases are compared. Two concepts, "enough resources" and "a lack of resources," are introduced and investigated. The theoretical results are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

A comparative analysis of the efficiency of various ways of organization of economic agents is carried out, taking into account the structure and regulations of their interaction in the models of the Cournot oligopoly. The Cournot oligopoly models in the form of a supply chain are constructed and analytically investigated, taking into account the green effect and concern for fairness. For symmetric models of the Cournot oligopoly with different ways of organization of economic agents, the respective structures of social and individual preferences are analytically obtained. A numerical study of the Cournot oligopoly models in various forms with asymmetrical agents has been carried out, and the corresponding structures of social and individual preferences have been obtained. [ABSTRACT FROM AUTHOR]

A brief description of the authors' concept of sustainable management is given. According to the concept, the sustainable development of an active system means that it satisfies some viability conditions and, at the same time, the interests of its active agents are considered and coordinated. The main emphasis is made on two mathematical examples. First, a relation between egoistic and altruistic evolutionary strategies is studied using the Verhulst–Pearl model. Second, selfish and cooperative types of behavior of users of a renewable resource are compared on the basis of a differential game model. The viability conditions are formalized as phase constraints. They can be satisfied through voluntary coordination of the agents or their enforced coordination provided by a specially introduced principal. The main contribution of the paper is a comparative analysis of these ways of sustainable management. [ABSTRACT FROM AUTHOR]

This paper presents a comparative analysis of the efficiency of organizational modes (information structures) for the interaction of economic agents in static and dynamic Cournot duopoly models. We compare the independent behavior of equal players, their cooperation, and the hierarchy formalized as Germeier games. The efficiency of individual players and the entire society is quantitatively assessed using the private and social relative efficiency indices. The ecological safety conditions of the system are investigated. An organizational and economic interpretation of the results is proposed. [ABSTRACT FROM AUTHOR]

Dynamic theoretic game models for the coordination of private and social interests of agents in the concept of the sustainable development (SD) of the dynamic system controlled by them are investigated. Within this concept, the hierarchical control mechanisms—methods of administrative control and inducement—are formalized as solutions of hierarchical differential games with the phase constraints reflecting the requirements for the state of the controlled dynamic system providing the conditions for SD. Administrative control involves the impact of the leading player (the subject of managing SD) on the set of admissible controls for the followers (the subject of the impact on the controlled dynamic system); and the incentive, on his payoff function. Mechanisms of administrative and economic management are formalized as computer imitation scenarios. The dynamic models considered in the article are the development of the models for the coordination of private and social interests proposed by Yu.B. Germeyer and I.A. Vatel. Numerical calculations are carried out and a comparative analysis of the effectiveness of these control mechanisms for the fisheries' model is fulfilled. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic game-theoretic statement of the resource allocation problem in an organizational system. The application of evolutionary modeling algorithms for solving such problems is considered. Some illustrative examples are given. [ABSTRACT FROM AUTHOR]

This paper analyzes conditions of system compatibility in the game-theoretic models of resource allocation between social and private activities. We describe economic and administrative control mechanisms for system compatibility. [ABSTRACT FROM AUTHOR]

We consider a stimulation model with Markov dynamics and discounted optimality criteria in case of discrete time and infinite planning horizon. In this model, the regulator has an economic impact on the executor, choosing a stimulating function that depends on the system state and the actions of the executor, who employs positional control strategies. System dynamics, revenues of the regulator and costs of the executor depend on the system state and the executor’s actions. We show that finding an approximate solution of the (inverse) Stackelberg game reduces to solving the optimal control problem with criterion equal to the difference between the revenue of the regulator and the costs of the executor. Here the ε-optimal strategy of the regulator is to economically motivate the executor to follow this optimal control strategy. [ABSTRACT FROM AUTHOR]

This paper studies a three-level control system. Impulsion serves as hierarchical control at the two levels of the system. We analyze the behavior of the system in the case of informational rules defined by the Germeier games Γ and Γ. Equilibrium design algorithms are proposed. The solution of the three-level differential model is reduced to the exploration of an equivalent multistep-differential model. [ABSTRACT FROM AUTHOR]

This paper considers particular classes of differential hierarchical two-player games in open-loop strategies. The games are interpreted as models of corruption and sustainable management in hierarchical systems. We formulate optimality principles for the above classes of games as modifications of Stackelberg equilibria. And finally, equilibrium design algorithms for the games are suggested and tested using a series of numerical examples. [ABSTRACT FROM AUTHOR]

Different approaches to studying hierarchical problems are compared with the use of a two-stage dynamic model of water quality control in the case of point pollution sources. Variations in pollutant concentrations in a watercourse are described by partial differential equations. The study embraces the cases of a single and multiple point pollution sources and different types of pollutants. [ABSTRACT FROM AUTHOR]

A new numerical method of solving nonlinear boundary problems based on collocational-type approximations is developed with examples of one- and two-dimensional stability problems for a viscoelastic shell. The method allows us to simplify significantly the arithmetization procedure of differential expressions with subsequent efficient computer implementation of the algorithm. A high degree of calculation accuracy is provided. The estimation of the efficiency of the new numerical scheme is obtained by comparing the results with data where the system was modeled using the method of finite differences and the Galerkin method. [ABSTRACT FROM AUTHOR]