Abstract: The article is devoted to the study of corruption in the previously studied static model of the combination of common and private interests (SOCHI model) of several agents, namely, corruption in the allocation of resources. The upper level – the principal – allocates resources to the elements of the lower level - agents - so that the latter distribute them between their general and their private interests. The middle level - the supervisor representing the interests of the top level - underestimates the amount of resources allocated to the agent, which he can increase by a certain amount, but no more than to the level initially set by the principal. A three-level hierarchical tree system is formed. This article examines a three-level hierarchical system in which the supervisor uses an economic corruption mechanism in the allocation of resources. Two approaches are used in the study of this mechanism: descriptive and optimization. The descriptive approach assumes that the functions of bribery in question are known. The optimization approach involves the use of Hermeyer's theorem. The influence of corruption in the allocation of resources on system consistency in the SOCHI model is investigated: it is proved that corruption in the allocation of resources can only reduce consistency in the SOCHI model. It is proved that economic corruption is always beneficial for agents, but it turns out to be manipulative for a supervisor. The only way to fight corruption in the allocation of resources has been found.

Abstract: The article is devoted to the study of corruption in the previously studied static model of the combination of general and private interests (SOCHI model) of several agents. In this article, special attention is paid to the study of economic corruption. To do this, an intermediate level is introduced into the previously considered two-level system between the Principal and the Agents - a supervisor who represents the interests of the Principal, but in exchange for a bribe can improve the position of the agent at the expense of the Principal. The latter sets for each agent, himself and the supervisor a share of participation in the total income. The supervisor can increase the agent's share in exchange for a bribe, reducing the Principal's share. This article examines a three-level hierarchical system in which the supervisor uses an economic corruption mechanism, in the study of which two approaches are used: descriptive and optimization. The descriptive approach assumes that the functions of bribery in question are known. The optimization approach involves the use of Hermeyer's theorem. The influence of economic corruption on systemic consistency in the SOCHI model is investigated: it is proved that economic corruption can theoretically increase consistency. But this requires the fulfillment of many conditions, the joint fulfillment of which is unlikely. It is proved that economic corruption is always beneficial for agents, and also for the supervisor. The only way to combat this kind of corruption has been found.

Abstract:  
This article is dedicated to examination of corruption in the previously researched static model of balancing common and private interests (SOCHI-models). In the previously considered two-level system, between the upper non-corrupted level and the lower – agents, is introduced the average level which in exchange for a bribe, can weaken the influence of the upper level. The upper level sets the minimum amount of resources for an agent to spend on general purposes. A supervisor, in exchange for a bribe, the role of which is played by the share of agent’s private income, can reduce this lower boundary, allowing the latter to spend more resources on private purposes. This article reviews the three-level hierarchical system “Principal-Supervisor-Agents”, where the supervisor uses the administrative corruption mechanism, which requires two descriptive and optimization approaches towards its examination. The descriptive approach suggests that the considered functions of bribery are known; while the optimization approach implies the use of Germeyer’s theorem. The author explores the impact of administrative corruption upon systemic congruence of the SOCHI-model: it is proven that the administrative corruption can only reduce congruence. The author finds the conditions that can beat or reduce administrative corruption can, as well as conditions when corruption is disadvantageous for supervisor or agent. The article determines the circle of agents that supervisor can exert influence upon.
 

Abstract: The article presents a dynamic socio-ecological-economic model of the synergetic development of individual economic entities, which makes it possible to reconcile their general and private interests. Maximization of specific consumption is proposed as a target parameter. Accordingly, in relation to private interests - the subject, in relation to general interests - the governing center. The model provides for the possibility of using the available resources by each entity both in the tasks of their own development and in the general development goals of other entities. The presented model can be used to form an economic development program for a separate territory, a separate industrial cluster, a municipality, a region and a macro-region. As a result of modeling, control parameters are formed for developing a strategy for economic development. A model of territorial development based on two models is presented: a dynamic model of the combination of general and private interests and a neoclassical Solow model. It is proposed to use a model for regional systems, where the elements of the system are regions within one macro-region. The parameters of the model used for the macroregion are described in terms of identification. The modification of the Solow model takes into account a) threshold limits on the volume of production in the region, emissions and discharges of pollutants from the regions; b) interaction of subjects in solving joint development problems through cross-investment for a synergistic effect; c) taking into account the influence of technical progress both on the volume of the quantity of products produced and on labor productivity. As for the use of the model of the combination of general and private interests, the sum of two terms was taken as the target function of agents (regions): the maximization of specific consumption is taken as the private interests of the region, and the specific consumption of the entire macroregion is taken as the general interest.

Abstract: The article is devoted to the development of a dynamic model for the coordination of general and private interests in the system of complex socio-ecological-economic synergetic development of a system of economic entities, the target control parameter of which is maximization of specific consumption. The parameters of the model under consideration are supposed to be supplemented with the criteria of ecological and economic sustainability of a group of subjects localized on a separate territory, within the boundaries of a separate industrial cluster, municipal formation, region or macroregion. The conditions for sustainable development (homeostasis) of the socio-ecological-economic system in the model are set by the requirements for the economic development of the agent, the maximum permissible emissions and discharges of pollutants into the environment in the process of economic activity. The resulting formalized dependencies make it possible to substantiate the environmental and social significance of the management decisions taken, as well as the effects associated with the dynamics and uncertainty of the external environment. The paper presents an algorithm for finding the Nash equilibrium in the previously presented dynamic model for combining general and private interests of territorial development. Some components of the vector of control actions are found analytically, for the rest an economical procedure is described. It is shown that in the absence of established threshold values for GRP and the concentration of pollutants in water and air, it is unprofitable for territorial entities to spend resources neither on investments in production or fixed production assets, nor on cleaning up pollution. Consequently, the expediency of introducing conditions for sustainable development, which are fulfilled by the subject in the form of equality, is shown.

Abstract: The article presents the results of approbation of the previously presented dynamic socio-ecological-economic model of the synergetic development of individual entities within the South Russian macro-region, which allows to harmonize the general and private interests of each region. The model is investigated on the materials of the Southern Federal District. The identification of the model for the macro-region of the Southern Federal District was carried out on the basis of the data of the website of the State Statistics Committee, which are in the public domain. For identification, the time series of 2005, 2010, 2015-2017 were taken. This choice is explained by both theoretical reasons (a step of five years was chosen for the long-term data and one year for the near-term data), and empirical (the data of the crisis periods of 2008 and 2012, as well as the years nearest to them, were not taken). As a result of the study, several controversial conclusions were drawn regarding the strategies of the subjects' behavior. Calculations show, in particular, that in the current conditions it is not profitable for any of the regions to develop its own production sphere; the optimal strategy for each of them is only to increase consumption in the hope of the production activity of neighboring regions. In view of the choice of this rational strategy by all regions at the same time, a general degradation of the production sphere and stagnation of the regional economy are predicted. At the same time, it was revealed that a further reduction in production becomes unprofitable for almost all lagging regions (the republics of the Southern Federal District), while the leading regions (the regions of the Southern Federal District) remain profitable for production inaction.