Publications

Bachet’s game is a variant of the game of Nim. There are 𝑛 objects in one pile. Two players take turns to remove any positive number of objects not exceeding some fixed number 𝑚. The player who takes the last object loses. We consider a variant of Bachet’s game in which each move is a lottery over set {1, 2, . . . ,𝑚}. The outcome of a lottery is the number of objects that player takes from the pile. We show that under some nondegenericity assumptions on the set of available lotteries the probability that the first player wins in subgame perfect Nash equilibrium converges to 1/2 as 𝑛 tends to infinity.

The debate on the increasing income and wealth inequalities in the USA and some other advanced economies often disregards the opposite trend, i.e. decreasing income inequalities between individuals throughout the entire world. The purpose of this chapter is to examine the potential trade-off between both trends and the role of globalisation in such a trade-off. Another important question relates to the impact of this trade-off on global governance. On the one hand, catch-up growth in emerging-market economies and the resulting decrease in global inequality can help reduce the economic and social sources of political conflicts and tensions between countries and enable their cooperation on various issues such as trade, environment, climate change, health, fighting terrorism, managing migration and many others. On the other hand, growing income inequalities within advanced economies can undermine the existing global political and economic order and boost protectionism and nationalistic egoism in many areas.

This paper studies the publication productivity of inbreds and non-inbreds among Russian academics. Existing literature provides ambiguous results on the relationship between inbred status and productivity. This may be explained by the use of different indicators for measuring publication productivity. We use data, which include indicators of both current publication productivity (at a certain point of time) and cumulative productivity (throughout the career) to identify whether inbreds and non-inbreds differ in their productivity. We did not find any difference in current publication productivity of inbreds and non-inbreds. We found, however, a difference in their cumulative publication productivity: non-inbreds are being more productive on an individual level throughout their careers. Although the conclusions are based on the Russian data, the analysis provides an explanation for existing contradictory results on the relationship between academic inbreeding and productivity in general.

We consider binary gas mixture flows with viscous compressible components in the absence of chemical reactions. We aggregate the previously derived regularized equations for inhomogeneous mixtures and thus derive new simpler regularized equations for homogeneous ones (i.e., with the common velocity and temperature). The entropy balance equation with the non-negative entropy production is stated for the new equations. They are constructed for numerical simulations of flows.

In this paper, we present all constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an arbitrary constant non-Abelian current in Euclidean space Rn of arbitrary finite dimension n. Using the invariance of the Yang-Mills equations under the orthogonal transformations of coordinates and gauge invariance, we choose a specific system of coordinates and a specific gauge fixing for each constant current and obtain all constant solutions of the Yang-Mills equations in this system of coordinates with this gauge fixing, and then in the original system of coordinates with the original gauge fixing. We use the singular value decomposition method and the method of two-sheeted covering of orthogonal group by spin group to do this. We prove that the number (0, 1, or 2) of constant solutions of the Yang-Mills equations in terms of the strength of the Yang-Mills field depends on the singular values of the matrix of current. The explicit form of all solutions and the invariant F^2 can always be written using singular values of this matrix. The relevance of the study is explained by the fact that the Yang-Mills equations describe electroweak interactions in the case of the Lie group SU(2). Nonconstant solutions of the Yang-Mills equations can be considered in the form of series of perturbation theory. The results of this paper are new and can be used to solve some problems in particle physics, in particular, to describe physical vacuum and to fully understand a quantum gauge theory.

Why do some newly introduced revolutionary governments face anti-government demonstrations and swiftly exit office, while others are able to establish political regimes that last for decades? Historical evidence finds revolutionary governments in the first decade of twenty-first century to be three times more vulnerable to mass protest than a hundred years ago. What can explain this trend? This paper relates the stability of newly emerged revolutionary governments to the political composition of the protest that brings a new incumbent to power and in factors that can shape it. Our theoretical model, incorporating protest into a dynamic Downsian framework, features the significant role of protest coordination, communication technology, ideology, and the coercive capacity of the regime. This paper contributes to the literature in several ways. First, it discusses a new historical trend of instability of revolutionary governments. Second, it proposes a model that helps to understand the growing instability of revolutionary regimes, as well as conditions that undermine stability. In equilibrium, it is possible to have a revolutionary government overthrown by popular uprising, despite the fact that it gained power on the wave of popular support. Third, under a set of conditions, the new incumbent would always come from a different part of political spectrum.

The chapter analyzes the influence of K. Marx's "Capital" on reformist Populism, legal Marxism and Katheder-sozialismus in Russia. Special attention is paid to heated discussions about the stages of Russia's economic development in comparison with Western Europe. 

Advance price announcements in the form of general rate increase (GRIs) by liner shipping companies have recently become the subject of investigations by competition authorities in different jurisdictions, including the European Union and Russia. The main goal of this paper is to answer the question whether GRIs predict price changes of competitors. Comparison of GRIs with actual price changes in particular routes, defined as antitrust markets in competition investigations in Russia, shows a limited anti-competitive effect of advance price announcements, albeit under specific market conditions. Regression analysis, undertaken in the context of the Russian investigation, rejects the hypothesis that the GRI of a particular company would be followed by price increases of its competitors. Moreover, the frequent changes in the market shares of liner companies support the hypothesis of competition vis à vis collusion. Remedies applied by competition authorities address content and timing of GRIs. The theory of tacit collusion suggests that remedies, which further specify the content of price announcements, may paradoxically enhance non-cooperative pricing, in contrast to remedies that restrict audience of GRIs by customers.

Ufnarovski remarked in 1990 that it is unknown whether any finitely presented associative algebra of linear growth is automaton, that is, whether the set of normal words in the algebra form a regular language. If the algebra is graded, then the rationality of the Hilbert series of the algebra follows from the affirmative answer to Ufnarovski’s question. Assuming that the ground field has a positive characteristic, we show that the answer to Ufnarovskii’s question is positive for graded algebras if and only if the basic field is an algebraic extension of its prime subfield. Moreover, in the “only if” part we show that there exists a finitely presented graded algebra of linear growth with irrational Hilbert series. In addition, over an arbitrary infinite basic field, the set of Hilbert series of the quadratic algebras of linear growth with 5 generators is infinite. Our approach is based on a connection with the dynamical Mordell–Lang conjecture. This conjecture describes the intersection of an orbit of an algebraic variety endomorphism with a subvariety. We show that the positive answer to Ufnarovski’s question implies some known cases of the dynamical Mordell– Lang conjecture. In particular, the positive answer for a class of algebras is equivalent to the Skolem–Mahler–Lech theorem which says that the set of the zero elements of any linear recurrent sequence over a zero characteristic field is the finite union of several arithmetic progressions. In particular, the counterexamples to this theorem in the positive characteristic case give examples of algebras with irrational Hilbert series.

As a result of the climate change the situation in Arctic area leads to several important consequences. On the one hand, fossil fuels can be exploited much easier than before. On the other hand, their excavation leads to serious potential threats to fishing by changing natural habitats which in turn creates serious damage to the countries’ economies. Another set of problems arises due to the extension of navigable season for shipping routes. Thus, there are already discussions on how should resources be allocated among countries. In Aleskerov and Victorova (An analysis of potential conflict zones in the Arctic Region, HSE Publishing House, Moscow, 2015) a model was presented analyzing preferences of the countries interested in natural resources and revealing potential conflicts among them. We present several areas allocation models based on different preferences over resources among interested countries. As a result, we constructed several allocations where areas are assigned to countries with respect to the distance or the total interest, or according to the procedure which is counterpart of the Adjusted Winner procedure. We consider this work as an attempt to help decision-making authorities in their complex work on adjusting preferences and conducting negotiations in the Arctic zone. We would like to emphasize that these models can be easily extended to larger number of parameters, to the case when some areas for some reasons should be excluded from consideration, to the case with ‘weighted’ preferences with respect to some parameters. And we strongly believe that such models and evaluations based on them can be helpful for the process of corresponding decision making.

In this paper we describe a methodology that allows researchers to measure empirically, in the form of well-defined indicators, the extent to which economic analysis and evidence is been applied in the enforcement of competition law, using data collected from the decisions of competition authorities. By mapping the value of these indicators to different legal standards, our methodology also allows one to identify the legal standards adopted in the assessment of different conducts that were investigated by the authorities. The policy implications of empirical work in this area are potentially very important, since the extent to which economic analysis is applied in the assessment of anti-competitive conduct by competition authorities may well influence the quality of this assessment (i.e. the quality of enforcing competition law, measured by the extent to which decision-errors and deterrence effects are minimised). Empirical analysis using the indicators can be used to undertake comparative analysis in different countries, to examine the extent to which authorities favour specific legal standards in the assessment of specific conducts and the way in which the judicial review process treats decisions depending on the legal standard used.

Objectives

The study examined the smokers’ non-compliance rates in indoor public places in Russia and the sociodemographic factors associated with non-compliance.

Methods

Univariate analysis and logistic regression models were performed using cross-sectional data from a representative sample of Russian adults (N = 4006).

Results

27.2% of Russian smokers did not comply with smoke-free bans. Non-compliance was attributed to sociodemographic characteristics of smokers, mainly to the number of cigarettes smoked per day, regular alcohol consumption, being aged between 15 and 34 years, being in the highest income group and living in an urban area. Neither the sex, nor the family status of smokers exerted a statistically significant affiliation with non-compliance. Higher rates of non-compliance were observed in restaurants, cafes, bars and nightclubs, common domestic premises of apartment buildings and indoor workplaces. Violations on public transport, in governmental buildings, health and sport facilities, colleges and universities were less common.

Conclusions

There is a need to revise the methods of enforcement with respect to sociodemographic characteristics of smokers associated with non-compliance in public places where violations are widespread.

We give a survey of approaches for analyzing the sensitivity of non-dominated alternatives to changes in the parameters of partial quasi-orderings that define preferences. Such parameters can include values of importance coefficients for different criteria or boundaries of interval estimates of the degrees of superiority in the importance of some criteria over others, boundaries of intervals of criteria value tradeoffs uncertainty, and others.

The modern mining industry has huge innovative potential for the introduction and development of digital revolution products. It has always been the most important industry of modelling development, as many operations and processes here are directly empirical and provide a large amount of data for quantitative analysis, which is now well suited to the use of digital intelligent technologies. With the development of digital technologies, effective integrated modeling techniques and the introduction of new process management, knowledge and data analysis tools are needed. Analytical models here are primarily designed to symbolize object properties in dynamics. Intelligent models and solutions based on the use of information technologies and methods of working with big data were becoming most popular, and the processes of integrated monitoring, personalization, risk management, search and generation of solutions, web orientation of programs and technologies and formation of network organizational structures of management were becoming particularly important. Mining enterprises have specific risks: mining and geological risks, risks of loss of market share and investment attractiveness due to biased valuation of useful fossil reserves, risks related to cybersecurity and innovation. Enterprises need to implement new technologies in a comprehensive manner, and information innovation is becoming very important in the face of a lack of financial resources. Expert systems, fuzzy logic, neural networks and genetic algorithms are the most relevant applications in international practice of geoinformation resource management, which largely determines the practical use of artificial intelligence methods and tools in interaction with pound-based management solutions. Modern analytical expertise includes the integration of process management systems, in particular those that are different, which is based on the development of a large number of integration technologies and techniques that apply different data models and are carried out through different procedures. The study examines the development of analytical models based on intelligent technologies, which are now increasingly used in various areas of the mining industry.

The paper develops a new extension of the sequential preference condition, which leads to unique stable matching in all subpopulations, obtained by consistent restrictions of the marriage matching problem. Under the new condition, the Gale–Shapley algorithm is stable, consistent, strategy-proof, Pareto optimal for men, and Pareto optimal for women.

The paper illustrates how a Bayesian approach to yield fitting can be implemented in a non-parametric framework with automatic smoothing inferred from the data. It also briefly illustrates the advantages of such an an approach using real data.

The paper uses an infinite dimensional (functional space) approach to inverse problems. Numerical computations are carried out using a Markov Chain Monte-Carlo algorithm with several tweaks to ensure good performance. The model explicitly uses bid-ask spreads to allow for observation errors and provides automatic smoothing based on them.

A non-parametric framework allows to capture complex shapes of zero-coupon yield curves typical for emerging markets. Bayesian approach allows to assess the precision of estimates, which is crucial for some applications. Examples of estimation results are reported for three different bond markets: liquid (German), medium liquidity (Chinese) and illiquid (Russian).

The result shows that infinite-dimensional Bayesian approach to term structure estimation is feasible. Market practitioners could use this approach to gain more insight into interest rates term structure. For example, they could now be able to complement their non-parametric term structure estimates with Bayesian confidence intervals, which would allow them to assess statistical significance of their results.

The model does not require parameter tuning during estimation. It has its own parameters, but they are to be selected during model setup.

This article analyses antitrust enforcement practice in Russian courts in the area of competition-restricting agreements. The analysis is based on the court decision database of litigations with the Russian competition authority (the Federal Antimonopoly Service (FAS)). In the database litigations that officially started in the period 2008–2012 were included. Final court decisions were evaluated, taking into account litigation duration (sometimes up to 3 years). The database contains 400 cases, including 236 horizontal agreements and 164 other agreements (mostly vertical agreements). Based on the evidence of this database, important features and problems of the interpretation and implementation of competition law in Russia and priority areas of enforcement were identified. Antitrust policy was analysed taking into account the risks of type 1 and type 2 errors, including the problem of flexibility of prohibitions (per se vs Rule of reason (ROR) approaches), standards of proof and the problem of consistency of enforcement.

The paper shows the possibility of applying the tool of non-additive measures and the belief functions theory to solving a number of problems of significance analysis and conflict of the political party positions. The study was performed on a database of online polls of parties in Germany before the elections to the Bundestag in 2013 and the results of these elections. The possibility of finding the most significant groups of issues for voting, evaluating the political heterogeneity of society, assessing the importance of the positions of individual parties for voting, assessing the conflict of the party positions on important issues is shown.

This article is devoted to the creation of intelligent modelling tools for decision support in the evaluation of intellectual projects submitted for financing, as based on qualitatively defined characteristics. The economic and mathematical models that form the basis of the toolkit are constructed using the mathematical apparatus of fuzzy logic, which allows for the description of poorly structured knowledge of specialists, as well as their application in solving questions about the extent of the impact of the proposed projects on the environment. The authors classify investment projects according to the degree of impact on the environment, the environmental criteria required by the investor for the evaluation of investment projects, and the formal formulation of the problem of evaluation of investment projects when taking into account the environmental factor. The toolkit was created based on the concept of intellectualization, where economic and mathematical models for the evaluation of investment projects are programmatically implemented via the tools and functions available in the MATLAB package.

We study alternative arbitrage strategies for stocks of Russian companies and the corresponding depositary receipts issued in European exchanges (‘mirror trades’). We provide evidence for significant arbitrage opportunities in Russia, and the potential returns are higher when the depository receipts are underpriced relative to stocks on the domestic market. Such asymmetry in arbitrage returns may be a consequence of money expatriation from Russia using these ‘mirror trades’ even when they are unprofitable, creating further mispricing. We also show that the long-short ‘buy-and-hold’ strategies, although being risky, generate returns which are about twice as high as the returns to the conversion strategies. Although the arbitrage returns have declined over time, they are still positive and generally higher than the market returns. Low liquidity of Russian depositary receipts on European exchanges is a significant barrier to arbitrage.