Dunaievskyi M. Mechanisms for improving the efficiency of decentralized systems and their application

The dissertation is dedicated to the study of decentralized systems, analysis and development of mechanisms to increase their efficiency based on mathematical algorithms and models, the application of the proposed solutions to real economic data of the regions of Ukraine. Scientific novelty and practical significance of the obtained results is the basis of development of innovative software and computer tools for quarterly assessment of economic efficiency and target structure of exports of the regions of Ukraine, which may be the basis of the macroeconomic decision support system. According to the developed algorithms, an assessment of the economic efficiency of the regions of Ukraine and the estimation of the optimal structure of exports for Ternopil region, Kirovograd region and Luhansk region were conducted. The proposed algorithms are the basis of the mechanisms for increasing the economic efficiency of regions, in particular, by borrowing the best management practices of leading districts. Developments regarding the theory and methodology of decentralized networks, in particular, supply chain networks (SC), information and communication networks, and economic decentralization of regions are presented. An innovative game model of a supply chain network consisting of a number of retailers of a product and a number of markets for that product was developed, where retailers compete non-cooperatively to maximize their expected profits by determining their optimal transactions for the product, as well as the optimal cybersecurity investments included in non-linear budget constraints. It is established that to solve the problem of finding equilibrium investments in cybersecurity of SC, it is possible to propose an iterative algorithm, which at each iteration gives an explicit relationship for product transactions, security levels and Lagrange multipliers associated with budget constraints. Stochastic methods of decision support under conditions of uncertainty are investigated. In particular, the application of Bass diffusion model of innovations to the spread of vaccinations is substantiated for the first time. The formula was obtained which allows to estimate the expected length of time until the moment of the initial purchase of an innovative product (receiving a vaccine against COVID-19) by an arbitrarily selected buyer (citizen). The influence of innovative buyers who make a decision to purchase (use) an innovative product immediately upon its appearance, as well as the influence of imitator buyers who make a decision to purchase (use) an innovative product with a certain lag, after the innovative product saturates the market and more information and feedback about it from innovative buyers is available, are took into consideration. Mathematical methods for supporting decision-making in the market of information and communication services and in state macrofunctions are researched. The reaction function of the follower (Internet service provider) to the decision of the leader (content of the provider) is established. Taking into account such basic parameters as the price of the service, the content provider's share of income, the market volume, costs per unit of expansion and maintenance of network capacity, the Internet service provider decides to what extent to expand the existing network capacity.