Goal of research: study of new organizational models and mechanisms, models of data analysis and decision-making, multi-criteria methods and social decision-making, as well as the application of the developed models and methods to different problems in the socio-economic, financial and political spheres.
Methodology: game theory and operations research, multi-criteria decision-making, individual and social choice theory, optimization, probability theory and mathematical statistics, cluster analysis, network data analysis, imprecise probability theory and others.
Empirical base of research: data on migrant flows collected UN Population Division; data on the observed air flows in the United States in the period 1995-1999; data on voting in the State Duma of the Russian Federation for the period 1996-2007; stock market data quotes S&P500 for the period 2001-2010; rankings of scientific journals of economics and management; roll-call votes in the Reichstag of the Weimar Germany in 1920-1933; data base of interstate conflicts; RCAP (Regulatory Compliance Assessment Programme) reports to assess of degree deviation of national regulation from the Basel minimum standards; data of the Bank for International Settlements; database of target prices of shares of Russian companies in 2012-2014.
Results of research:
- within the framework of research to identify the influence in network structures several models are proposed which take into account individual attributes of nodes, the intensity of long-range interactions and group influence; the proposed models have been applied to real networks of migration flows and food exports;
- the network approach with a new index of the influence (long-range interaction centrality, LRIC), taking into account the indirect interaction of the network, is applied to the analysis of military conflicts and wars involving different countries;
- a model based on the superposition principle was applied for tornado prediction; a comparison of results of our model and other existing techniques of tornado prediction was made;
- a new approach to the analysis of complex systems based on the construction of the family of clusterings, whose properties allow us to identify some of the important substantive features of the original system is proposed; the feasibility and applicability of the developed approach are illustrated by the analysis of voting in the Russian State Duma and the analysis of stock market indices;
- a mathematical model for the problem of optimally composing the teaching personnel at a college to run online courses has been developed, and numerical evaluations of such compositions with the use of the model have been conducted;
- mathematical models for estimating the expediency of investing in developing a regional electrical grid and the time of the cost recuperation (the payback time) of a system for storing electricity by residents of a micro region of a city being a part of a regional electrical grid have been developed;
- a mathematical model underlying a system for optimizing the recycling of municipal solid waste products has been developed;
- the problem of mechanism design in a health care market regulation has been investigated; the conditions of efficient solution have been described; it is shown that the market equilibrium cannot implement an efficient solution;
- the problem of the seeding method in a knockout tournament has been investigated; a new set of axioms and new method (equal gap seeding) are proposed;
- a generalized auction model has been developed; comparative statics of auction outcome with respect to the distribution of bidders types has been obtained; the variation of distribution is modeled by different notions of stochastic orders, both univariate (independent types) and multivariate (interdependent types); the main results hold for the generalized auction model;
- a new approach to the formation of conciliatory solutions in the problems of multicriterial choice based on the concept of maximum likelihood optimal (briefly, mp-optimal) alternatives has been developed; properties of these alternatives were investigated and methods for their search were identified;
- quantitative estimates of (in)consistency are obtained for three ratings of Russian economic journals, that have been independently proposed by Muravyev (2012), Balatsky (2015) and researchers from the Higher School of Economics (2014); additionally, these three orderings are compared to journal rankings based on values of Science Index and 2- and 5-year impact factors published by eLIBRARY.ru; it is demonstrated that all journal orderings weakly, though positively, correlate with each other;
- Pareto principle and majority rule based solution concepts, such as the Copeland rule, the Pareto set, the core, the uncovered set and the minimal externally stable set, has been applied to produce aggregate rankings of 74 top Russian economic and management journals; correlation analysis has demonstrated that aggregate rankings reduce the number of contradictions and represent the set of initial three rankings better than any of the latter;
- manipulability of social choice rules under incomplete information, particularly, the influence of different public information types on the manipulability, is studied; it is proved that the probability of manipulation is not changed, comparing to the complete information case, if a social choice rule is strongly computable from the given poll information function (PIF); algorithms and methods for calculating the coalitional manipulability of voting rules for the cases when voters in one coalition have different preferences, have been developed;
- using the indices of pairwise consistency of the members of elected bodies, the influence on political decisions was estimated, using as an example the Reichstag of the Weimar Germany 1919-1930; it is shown that the readiness to form a coalition gives the participants an opportunity to increase their influence on political decision-making, while the existence of restrictions on the formation of coalition or unpopular political program does not provide full realization of this influence on decisions;
- the multidimensional index is developed and studied to an analysis of polarization of social (political) system; this index is used to analyze the Russian State Duma (1994-2003) and the United States House of Representatives;
- within the study of standards of the Basel Committee it has been shown that a single regulation in banking sphere may cause negative consequences for the economy, especially for the recipient countries; quantitative analysis of the factors that can be used during the transition to Basel III standards for the formation of the transitional institutions to take into account the level of economic development of the countries proposed;
- network approach to assessment of systemic risk in the market of international borrowings has been developed; the proposed method makes it possible to determine the country, which at first glance do not have a high level of systemic importance, but at the same time have a significant influence on stability of the system as a whole;
- new models of the interaction of small and medium price-taking traders on a stock exchange has been proposed for the case of traders dealing with derivative financial instruments (such as futures and options contracts); conditions of an existence of a guaranteeing strategy for a trader in the zero-sum game with the exchange have been obtained; illustrative examples for a trader searching the best guaranteed result of a trade on the stock exchange were given;
- in the framework of belief function theory the consistency of the recommendations of investment banks on the value of the shares of Russian companies in 2012-2014 was studied using game-theoretic methods (Shapley index, interaction index), methods of network analysis, methods of analysis of fuzzy relations, using hierarchical clustering.
Level of implementation, recommendations on implementation or outcomes of the implementation of the results.
Both fundamental and applied results have been obtained. Most applicable results have an analytical and a recommendation character.