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Of all publications in the section: 70
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Working paper
Podinovski, Podinovskaya O. V. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2014. No. 04.
Hierarchical structures are frequently used to formalize complex multicriteria decision analysis problems. The analytic hierarchy process (AHP) of Saaty (1980) is an established method used to solve practical multicriteria problems of the hierarchical nature. It is also well-known that AHP, and its modifications and generalizations poses a number of fundamental drawbacks that cannot in principle be overcome. The main drawbacks are the independence of the evaluation procedure of the criteria importance from the normalization of criterion values – this violates the requirement of the mathematical theory of measurement, and the lack of a formal definition of the notion of criteria importance. Furthermore, the use of ratio scales in AHP for the expression of importance of criteria is theoretically unsubstantiated. We suggest a new methodology suitable for the analysis of multicriteria problems with hierarchical structures. It is based on criteria importance theory.
Added: Apr 24, 2014
Working paper
Rubchinskiy A. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2015. No. WP7/2015/09.
An algorithm of solution of the Automatic Classification (AC for brevity) problem is set forth in the paper. In the AC problem, it is required to find one or several partitions, starting with the given pattern matrix or dissimilarity / similarity matrix. The three-level scheme of the algorithm is suggested. The output of the procedure is a family of classifications, while the ratio between the cardinality of this family and the cardinality of the set of all the classifications, considered in the procedure, is taken as a measure of complexity of the initial AC problem. For classifications of parliament members according to their vote results, the general notion of complexity is interpreted as consistence or rationality of this parliament policy. For “tossing” deputies or ⁄ and whole fractions the corresponding clusters become poorly distinguished and partially perplexing that results in relatively high value of complexity of their classifications. By contrast, under consistent policy, deputies’ clusters are clearly distinguished and the complexity level is low enough (i.e. in a given parliament the level of consistency, accordance, rationality is high). The mentioned reasoning was applied to analysis of activity of 2-nd, 3-rd and 4-th RF Duma (Russian parliament, 1996–2007). The classifications based upon one-month votes were constructed for every month. The comparison of complexity for selected periods allows suggesting new meaningful interpretations of activity of various election bodies, including different country parliaments, international organizations and board of large corporations.
Added: Oct 19, 2017
Working paper
Subochev A. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2008. No. 3.
Twelve sets, proposed as social choice solution concepts, are compared: the core, five versions of the uncovered set, two versions of the minimal weakly stable sets, the uncaptured set, the untrapped set, the minimal undominated set (strong top cycle) and the minimal dominant set (weak top cycle). The main results presented are the following. A criterion to determine whether an alternative belongs to a minimal weakly stable set is found. It establishes the logical connection between minimal weakly stable sets and covering relation. In tournaments and in general case it is determined for all twelve sets, whether each two of them are related by inclusion or not. In tournaments the concept of stability is employed to generalize the notions of weakly stable and uncovered sets. New concepts of k-stable alternatives and k-stable sets are introduced and their properties and mutual relations are explored. A concept of the minimal dominant set is generalized. It helps to establish that in general case all dominant sets are ordered by strict inclusion. In tournaments the hierarchies of the classes of k-stable alternatives and k-stable sets combined with the system of dominant sets constitute tournament’s structure (“microstructure” and “macrostructure” respectively). This internal structure may be treated as a system of reference, which is based on difference in degrees of stability. An algorithm for calculating the minimal dominant sets and the classes of k-stable alternatives is also given.
Added: Dec 26, 2012
Working paper
Iskakov M., Iskakov A. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2012. No. 06.

A new concept of equilibrium in secure strategies (EinSS) in non-cooperative games is presented. The EinSS coincides with the Nash Equilibrium when Nash Equilibrium exists and postulates the incentive of players to maximize their profit under the condition of security against actions of other players. The new concept is illustrated by a number of matrix game examples and compared with
other closely related theoretical models. We prove the existence of equilibrium in secure strategies in two classic games that fail to have Nash equilibria. On an infinite line we obtain the solution in secure strategies of the classic Hotelling’s price game (1929) with a restricted reservation price and linear transportation costs. New type of monopolistic equilibria in secure strategies are discovered in the Tullock Contest (1967, 1980) of two players.

Added: Dec 16, 2012
Working paper
д’Апремон К., Дош Сантош Феррейра Р. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2012. No. 02.

We present a comprehensive model of household economic decision covering both fully cooperative and non-cooperative cases as well as semi-cooperative cases, varying with income distribution and a parameter vector θ representing degrees of individual autonomy with respect to the public goods. In this model, the concept of “household θ-equilibrium” is introduced through the reformulation of the Lindahl equilibrium for Nashimplementation and its extension to semi-cooperation. Existence is proved and some generic properties derived.
An example is given to illustrate. Finally, a particular decomposition of the pseudo-Slutsky matrix is derived and the testability of the various models discussed.

Added: Dec 16, 2012
Working paper
Aleskerov F. T., Tverskoy D. N. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2014. No.  WP7/2014/05.
The problem of the unicellular-multicellular transition is one of the main issues that is discussing in evolutionary biology. In [1] the fitness of a colony of cells is considered in terms of its two basic components, viability and fecundity. Intrinsic trade-off function of each cell defines a type of cell. We elaborate models providing in [1]. Assuming that all intrinsic trade-off functions are linear, we construct a model with different cell types and show that the differentiation of these cell types leads to full specialization. In addition, we attempt to consider the fact that environmental factors influence the fitness of the colony. Thus, we introduce an energy restriction to the model and show that the situations can be observed where some cells continue to be specialized while other cells become indifferent between the states in which they can be specialized or unspecialized. It is worth pointing out that the models from [1] are not robust. We try to overcome this disadvantage.
Added: Sep 23, 2015
Working paper
Aleskerov F. T., Subochev A. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2009. No. 3.
A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose several new versions of solution sets.
Added: Dec 26, 2012
Working paper
Shvydun S. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2015. No. WP7/2015/07.
Two-stage superposition choice procedures, which sequentially apply two choice procedures so that the result of the first choice procedure is the input for the second choice procedure, are studied. We define which of them satisfy given normative conditions, showing how a final choice is changed due to the changes of preferences or a set of feasible alternatives. A theorem is proved showing which normative conditions are satisfied for two-stage choice procedures based on different scoring rules, rules, using majority relation, value function and tournament matrix. A complexity of two-stage choice procedures as well as its runtime on real data are evaluated.
Added: Oct 20, 2015
Working paper
Aleskerov F. T., Yakuba V. I. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2017. No. 01.
Several models of migrants’ allocation in settlements allowing not to increase a polarization considerably in the society are proposed. Models are illustrated via examples.
Added: Oct 11, 2017
Working paper
Sandomirskaia M. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2016. No. 1.
The paper examines an interaction of boundedly rational agents that are able to calculate their benefits after reaction of an opponent to their own deviations from the current strategy. Accounting for strategic aspects of interaction among players can be implemented as a generalization of the Nash equilibrium concept. This is a possible compromise behavior: not absolutely myopic as Nash concept and not as wise as supergame approach. This leads to a farsighted equilibrium concept that we call a Nash-2 equilibrium. We prove the existence of Nash-2 equilibrium for almost every 2-person game and discuss the problem of possible multiplicity of such equilibria. For a number of models (Bertrand duopoly with homogeneous and heterogeneous product, Cournot duopoly, Tullock contest) the Nash-2 equilibrium sets are obtained and treated as tacit collusion or strong competition depending additional security considerations. For n-person games the idea of selective farsightness is introduced by means of reflection network among players. Examples demonstrate that the reflection network topology fundamentally affects possible equilibria.
Added: Mar 3, 2016
Working paper
Kaplan T. R., Zamir S. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2012. No. 01.

In the framework of a ﬁrst-price private-value auction, we study the seller as a player in a game with the buyers in which he has private information about their realized valuations. We ask whether the seller can beneﬁt by using his private information strategically. We ﬁnd that in fact, depending upon his information, available signals, and his commitment power, he may indeed increase his revenue by strategic transmission of his information.

Added: Dec 16, 2012
Working paper
Smirnov A. D. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2012. No. 05.
The proposed model is aimed to reveal important patterns in the behavior of a simplified financial system. The patterns could be detected as regular cycles consisting of debt bubbles and crises. Financial cycles have a well defined structure and form periodic sequences along the axis of credit expansion while retaining stochastic nature in terms of time. Bubbles are defined as “large asset price deviations” from their fundamental value, and crises, if would represent huge losses of financial wealth. Regular sequences of bubbles and crises in the model are explained via behavior of market participants whose collective actions facilitate either emergence or  postponement of crises due to events as investors’ self-imposed restrictions upon debt accumulation. The paraphrase of famous Hamlet’s dilemma exposes the illusory character of investors’ attempt to avoid crises: financial catastrophes, even being postponed, are inevitable under the regime of credit expansion. It was shown, in particular, that the probability of default grows in coherence with the increasing money issuance, and at the point of a total collapse it reaches the unit value.  The model clearly discerns phases of normal investing, speculation and a Ponzi game which have the same meaning as in the “financial instability hypothesis” elaborated by H. Minsky. The model while supporting the assessment of crises inevitability under regime of a credit expansion, does not share the  Austrian School doomsday predictions regarding the exact dates of such events.
Added: Dec 16, 2012
Working paper
Чистяков В. В., Гончаров А. А. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2010. № 04.
Added: Mar 23, 2013
Working paper
Калягин В. А., Чистяков В. В. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2009. № 01.
Added: Mar 23, 2013
Working paper
Алескеров Ф. Т., Гохберг Л. М., Егорова Л. Г. и др. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2012. № 07.
Analysis of the science, education and innovation data is very difficult and complex problem. In this paper we describe the method of pattern analysis and the results of its application to the problem of analyzing the development of science, education and the success of innovative activity in the regions of the Russian Federation. In this study we examined characteristics of the regions of Russia such as the level of socio-economic conditions and the potential and efficiency of science, education and innovation from 2007 to 2010. Also we obtain a classification of regions by the similarity of the internal structure of these indicators, constructed trajectories of regional development over time, and found groups of regions carring out similar strategies.
Added: Dec 16, 2012
Working paper
Погорельский К. Б. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2010. № 01.
In this paper I investigate the results of the recent Quota and Voice Reform, adopted by the International Monetary Fund in April 2008, by means of formal voting power analysis. Using classical and preference-based power indices, I demonstrate that although the relative changes in power of some members are basically in line with the stated goals of the Reform (e.g., more voice for the low-income countries), the resulting power re-distribution is hardly significant, if viewed in absolute terms. I argue that the main reasons for this situation are the current distribution of quota shares and the substantially limited ability of the Fund to act, which results from the supermajority decision making rule requiring an immense degree of support among members for any reallocation of the quotas to come into force.
Added: Mar 23, 2013
Working paper
Якуба В. И. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2003. № 03.
Added: Mar 21, 2013
Working paper
Кисельгоф С. Г. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2011. № 01.
Added: Dec 25, 2012
Working paper
Zakharov A. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2008. No. 01.
What was the main factor behind the pro-Kremlin United Russia winning the December 2007 State Duma election with 64% of the seats? The party’s centrist ideology, association with Vladimir Putin, as well as media bias, administrative pressure, and vote-rigging have all been suggested as the primary cause behind the party’s success. This work tackles the question by estimating a multinomial logit model of voter choice based on survey data from May 2007. The paper finds the approval of President Putin tends to be the single most important factor affecting the voter’s choice in favor of United Russia. The personal ideological preferences was a major factor affecting the vote, so the party’s centrist position improved its electoral performance. The opponents’ appeal to older voters also was a contributing factor. Voter’s income, education, and the rural/urban status were found to have little effect on the vote.
Added: Mar 23, 2013
Working paper
Treisman D. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2007. No. 06.
In this paper, I review the main trends in voting in national elections in Russia since 1991, discuss the evidence of manipulation or falsification by the authorities, and use statistical techniques to examine the determinants of voting trends. The emphasis is on explaining change over time in the vote shares of different parties or groups of parties, not on identifiying social, economic, or opinion correlates of individuals’ party choice at a given point in time—a subject that has been well-studied in previous work by various scholars. My goal is to provide a relatively comprehensive introduction to the changing electoral landscape in the two decades since the birth of the independent Russian state. The paper offers a more detailed and technical examination of the evidence that is summarized in Chapter 10 of my book manuscript titled The Return: Russia’s Journey from Gorbachev to Medvedev.
Added: Mar 23, 2013
Working paper
Кремер М., Maskin E. S. Математические методы анализа решений в экономике, бизнесе и политике. WP7. Высшая школа экономики, 2007. No. 01.
The theory of comparative advantage predicts that, with expanding global markets, income inequality in poorer countries should decrease. To date, however, the international record on inequality is at best mixed in the face of recent globalization. In this paper, we outline an alternative theory that seems more consistent with what has actually happened.
Added: Mar 23, 2013