The authors highlight the high priority of rationalization in the management of the totality of transactions carried out in the sphere of network retail, in close contact with the service consumer. For network retail objects with a shift trading function, it is important to implement a direct and permanent impact, both on the system structure and on the basic processes in the area of mass trade services. This impact focuses on studying the flow of requests, service inputs and outputs of the system, as well as the length of waiting times, and the length of queues. The success of development in such retail networks depends on the flexibility of the operations performed by the contractor in close contact with the service consumer. It is envisaged to consider peculiarities in the rationalization of network retail management with trade turnover (flexibility) functions. The latter define the structure of the service delivery system for service consumers with processes running, in which client demands for services, as defined in the income chain, even though the intensity of the customer service flow is not constant. The purpose of the research is to present the informative field for rationalization in network retail management with the function of shifting trade, based on the mathematical description and repeated «playing» of all processes within the area of mass service. To represent the informative area for rationalization in network retail management with a shift trading function based on a mathematical description and repeated play of all processes within the public service area, Methods of probability theory and mathematical statistics have been used, as well as cloud computing in AnyLogic Claud environment, AnyLogic service. The results of the study was the presentation of new possibilities for rationalizing network retail management by groups of network objects based on the concept of a mass service area, and in view of the fact that there is an n-channel system of mass service with an unlimited queue, where the request flow has the intensity λ, and the service flow is the intensity μ. The study was implemented with the example of one of the hubs Walmart-Salvador, uniting 90 supermarkets of the company. All Walmart hubs combine only the same supermarket type, supporting the trade changeover function within a single graph (half-yearly). Similar Walmart hubs are developed in Mexico, Great Britain, Brazil, China, Canada, South Africa, Chile, Japan, Costa Rica, Guatemala, Argentina, Honduras, Nicaragua, El Salvador, and Ukraine. At the same time, all network nodes contain objects that apply multi-channel service systems, most common in the network retail with an unlimited queue and an option to add a new service node. It is the Walmart-Salvador hub that has a fairly high percentage of customers’ refusals due to the busy service devices (this estimate ranging from 19% to 25%). As a result, Walmart’s lost annual profit reaches up to USD 25.5 million approximately. The rationalization in the management of the network retail for the Walmart-Salvador hub objects is implemented with a breakdown into 8 groups, united according to common input parameters, the latter providing a solution for the optimal number of service devices, and their required reserve and runoff are calculated, as well as efficient productivity resulting from the consistency of the input and output flows in the service channel and the stability in the mass service system. At the same time, programming for solving the problem of the management rationalization is realized using rate fixing for the basic processes in the area of mass service. In this way, mass service system sustainability is ensured, with the average timing for the application staying in the mass service system being crucial. In particular, implementing such a standard could allow avoiding losses caused by waiting for servicing and unproductive ones. Among other relevant factors are: associated timing, probability or other values (necessary for transformation operations in the characteristics of the mass service area, performed for generating target values of this indicator). Perspectives of implementing the mathematical description of the processes in a mass-service area are in the fact that it will provide for significantly simplification in the processes of rationalizing the retail management in shift-trading facilities, regardless of the frequency of quantity and quality product range changes.

The objective of the article is to determine the potential of blockchain technologies in various sectors of the digital economy, in the case of the countries of the European Union. Methodology. The research assesses the use of digital technologies to ensure the country's digital development, based on data from the European Commission and the Digital Economy and Society Index (DESI). On the basis of DESI, a cluster diagram was created to determine the potential for the use of blockchain technology in the countries of the European Union. Results. The potential for the use of blockchain technology in each country depends and is significantly connected with the introduction of different technologies and the availability of the Internet, the provision of digital services by the government, the development of human capital. The main potential advantages of the technology include the following: acceleration of globalization processes, ensuring the country's transition from real production to technological development, change of established business models, transformation and optimization of value chains of different sectors of the economy by reducing costs; transformation of the nature of mediation due to technological changes; the use of cryptocurrency to achieve the consensus of economic agents on the allocation of scarce resources on a global scale.

The conditions for doing business at this stage are often similar in a game in which you need to calculate your actions a few steps ahead. At the same time, it is important to highlight several possible current options and make the necessary decision at the control moment. Moreover, each of the options formed should be justified, understandable and take into account the risk factors and available resources.Today, the main problem of assessing and minimizing the risk of “unfriendly takeover” is due to the fact that in most cases the raider is a player who acts quite legitimately and relies on the loopholes of the current legislative framework. Therefore, it is easier to identify possible actions of the raider and to avoid them within the limits of the reverse game than to deal with the consequences.The purpose of the research is to study the specificity of the individualized assessment and minimization of the risk of “unfriendly takeover” by using elements of game theory.It has been taken into account that the effect of individualization in assessing the risk of unfriendly takeover of enterprises can possibly be achieved on the basis of the application of game theory, the elements of which provide simulation of the unfriendly takeover process within the mathematical description of the inherent combinations of attack/defence as if they actually occurred in time both within one state of the external environment and for their given set.The results allowed forming mathematical decision-making models based on the elements of the antagonistic game “raider-target enterprise” and “raider games with the external environment”, which proved the possibility to: 1) identify possible functions of wins/losses; 2) combinations of attacks that can be neglected (that is, from the point of view of the rationality of decisions, will be rejected by the raider); 3) the ranking of the raider’s “attack combinations” for the reliability of their use during “unfriendly takeover”. Under such conditions, the target company can provide not only a detailed assessment, but also an effective minimization of the risk of “unfriendly takeover” and allocate the best combination of protection.

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О. О. Маслиган, д. е. н., доцент кафедри менеджменту, управління економічними процесами та туризму, Мукачівський державний університет О. О. Королович, к. е. н., доцент кафедри обліку і оподаткування та маркетингу, Мукачівський державний університет Н. С. Ліба, д. е. н., професор кафедри обліку і оподаткування та маркетингу, Мукачівський державний університет Ю. В. Терешко, к. е. н., доцент кафедри економіки та цифрового бізнесу, Державний університет інтелектуальних технологій і зв'язку СУЧАСНИЙ ІНСТРУМЕНТАРІЙ МОДЕЛЮВАННЯ ФІНАНСОВОГО РИНКУ У СЕРЕДОВИЩІ MATHEMATICAThe financial market is a complex system influenced by a significant number of signs-factors, and its functioning is determined by a significant number of signs-results. The complexity of the model leads to the fact that when building financial market models, it is necessary to use different types of systems of the one-dimensional equations, which the model can contain from 2 to n equations, so it is difficult to form and study them not far too modern means and tools of symbolic mathematics. It is important to note that the means and instruments of symbolic mathematics, which are summarized in the Mathematica program, may quickly draw up a model of the financial market. Therefore, the study is a general description of financial market modeling tools using systems of the same equations in MATHEMATICA. The study uses methods of analysis, synthesis, and logical analysis. As part of the study, note that a model consisting of unidentified or difficult-identified equations cannot be the subject of the study, because it is considered to be of poor quality. According to the results of the study, it is proved that the MATHEMATICA program implements the mathematical expressions works included in the financial market model until it forms more identical or identical sets of equations. The program MATHEMATICA implements the study of the financial market model using the indirect method of the smallest squares and the following algorithm of actions: -form the primary form of the financial market model to identify the form of its equations; start the process of model equalization analysis by the method of the smallest squares; systematization of equality assessments for the structural form of the financial market model. Evaluation of over-identified equations by the method of the smallest squares can be stopped at the second step, as it is evidence of the quality of all the stipulated variables. The prospects of further research lie in the development of methods of modeling the financial market using uniform systems of equations and means of symbolic mathematics.