DETERMINATION OF PRIORITIES OF PLAYERS IN PARTIALLY CONFLICT SITUATIONS AND INVERSE PROBLEMS OF GAME THEORY

DETERMINATION OF PRIORITIES OF PLAYERS
IN PARTIALLY CONFLICT SITUATIONS
AND INVERSE PROBLEMS OF GAME THEORY

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 6-8

In the series of the game theory problems the players try not only to maximize their own utility function, but also to reduce (or, to the contrary, to increase) utility functions of other players. Thus the players' priorities are often not known, but their behaviour strategies, for example, strategies leading to Nash equilibrium, are known. For this case, in this paper the definition and solution of the inverse problems of game modelling allowing to determine the players' priorities are being proposed. The inverse problems of the game theory allow to define the character of relations between the players and to solve a number of forecasting and control problems in conflict situations. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 8-11

The problem of evaluation and forecasting of market capacity dynamics for RF’s regions, using the methods of pattern recognition by integral indicators is considered. All regions are divided into k classes. The integral indicators are calculated as

, where

– the weight of corresponding particular criteria

, obtained from standard macroeconomic indices for some years. On the basis of committee decision rules the methods of pattern recognition are developed, which allow correcting the apriori classification according to whole available information about socio-economic state of regions. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 11-15

In this report we concern the problem of state reform in Russia. We apply to this problem the methods of system analysis, interdisciplinary approaches and computer simulation. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 15-19

Моделирование взаимовлияния энергодобавыющих и энергопотребляющих отраслей (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 19-25

The focus of this paper is on three important issues concerning Russian banking: stability of financial system, the prevailing patterns of bank performance and the structural dissimilarities. In order to examine these issues the methodology of dynamic cluster analysis is applied. The research is based on the data analysis of 1018 Russian banks during nearly 5 years (March 1999 – September 2003). Some potential applications to regulatory surveillance in commercial banking are discussed. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 26-28

A clustering of the electoral outcomes is made in the parliamentary elections in the constituencies of Great Britain in terms of the relative support of the main parties. The over-time stability of the parties support in constituencies is analyzed. The same problem is solved for seven most recent Finnish municipal elections. It turns out that only very few classes are needed to characterize the average patterns of support distribution. Our main finding is that out of thousands of conceivable over-time trends only few are needed to characterize the support development in all three countries. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 28-31

The mathematical model of management of liquidity of bank have been built. The economy rate of growth is considered to be constant, while interest rates of short instruments osculates randomly. It is supposed, that the bank maximizes the expected net present value. The concept of optimal strategy of bank is entered. It is shown, that optimal strategy should satisfy Bellman equation. Solution of the equation is found in an explicit form. Various strategies of bank are considered depending on how the income of bank depends on random values. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 31-35

A resource supportability model for a stochastic network project of PERT type, is considered. The duration of each activity is random, and the corresponding probability density function is pregiven. Certain activities entering the project require extremely costly and rare resources (call it A-resources) which have to be prepared and delivered from outside and can be at the project's disposal within a short time span. Other activities require constrained renewable resources (B-resources), which are at the disposal of the project and are in limited supply for each type of resources. (full text)

THE REFLECTION THEORY AND ITS APPLICATIONS:
THE ROLE OF CONSCIOUSNESS IN OVERCOMING OF IRRATIONAL AIMS
AND ACTIONS ON THE STOCKHOLM SYNDROME EXAMPLE

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 35-38

Consciousness helps to manage the defense reactions of subconsciousness aimed at reactive behavior that is generally invariable. This phenomenon is illustrated on the example of Stockholm syndrome and is explained from the point of view of the reflection theory. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 38-39

In the last two decades several proposals of rankings over opportunity sets have been made on the basis of the intrinsic value of freedom of choice. A common characterisitic of many of those rankings is that they are extensions of the strict inclussion relation over sets. This responds to the intuition that an enlargement of the opportunity choice leads to an increasement of the degree of individual freedom. The paper proposes economically meaningfull representation results for a family of orderings over sets that includes most of the rankings mentioned above. (full text)

NONLINEAR NATURE OF HUMAN RESPONSE ON ADVERTISING AGITATION.
EFFECTIVE FREQUENCY. SYNERGETIC AND ADVERTISING

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 39-41

Considered is the problem of the minimal number of repetitions enough for stimulating the consumer to buy. Introduced is the definition of the advertising response function and studied its main properties. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 41-45

Time series comparison between S&P500 data in 1997 and 1998 has been conducted. Phase trajectories and the corresponding density histograms were built. It turned out that the ratio of distances between neighboring regions of maximum density of the phase trajectories is determined by the Feigenbaum constant αF = 2.5029… The latter characterizes splittings of phase trajectory in a series of period-doubling bifurcations in the way from order to chaos for many nonlinear dynamical systems. Thus, αF can be used in forecasting stock indices behavior. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 45-48

The life cycle of a newly designed product is considered. The problem is to reallocate the company's expenses within the product's life cycle in order to maximize the company's profit. Thus, we deal with optimal budget reallocation within product's life cycle, including the sub-period of designing and creating the new product, as well as the sub-period of distributing the manufactured product on the market. Here the problem deals mostly with determining the product's selling price. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 48-50

The balancedness of a legislature described by a signed graph is studied. A new approach to the evaluating of relations among groups in the legislature is used based on the calculation of the index of concordance. The model is used for the analysis of the lower chamber of the Russian Parliament from January1994 to May 2003. (full text)

Evaluation of power of groups and fractions
in the Russian parliament (1994-2003)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 50-52

The problem of evaluation and the analysis of distribution of power is considered in the State Duma of the Russian Federation for 1994 – 2003. Banzhaf power index is used to evaluate the power of fractions and groups in the Russian Parliament for the simple majority decision making and under different assumptions about admissible coalitions. It is analyzed how the index is changed under different changes in structure of fractions and groups and under different scenarios of coalition formation. The dependence in the changes of index values is compared with respect to political events during this period. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 52-54

The paper presents approach to analysis and considers the model of the mobile service competitive market. The model includes a dynamic competition between two major operators, dominant operator and the others. The method for identification of the market carrying capacity is considered. The obtained results can be used in research to forecast and improve decision making in real dynamic systems. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 58-61

A model describing health condition levels of a large Siberian chemical plant worker is presented. All workers are divided into 3 groups: the healthy, risk group and unhealthy (mostly suffering from occupational diseases). The model describes transitions between the groups. The control task is to reduce the number of unhealthy groups through the implementation of various medical, preventive and social investments. The identification of the model parameters is carried out on the bases of statistical data and numerical experiments. The solutions of the model system essentially depend on the efficiency of the controls. The optimal control problem is solved numerically. The behavior of the optimal controls and states shows that during the initial years we have to invest more money in the treatment of the workers and then spend the maximum amounts possible for health protection. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 61-63

The study of electoral preferences stands among the most developed areas of politology. Yet there is a lack of generalized indexes that characterize different aspects of political system structure and evolution. (full text)

NONLINEAR MODELS IN INVESTIGATION SOCIAL AND
ECONOMICAL PROCESSES IN RUSSIA IN THE BEGINNING
OF THE XX CENTURY

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 63-66

Возможности синергетики в задачах изучения неустойчивых, переходных процессов исторического развития привлекли внимание историков в начале 1990-х гг. Отметим, что уже на рубеже 1980-90-х гг. историки-методологи отмечали, что "в настоящее время историки не имеют в своем распоряжении объективной, формализованной теории для перехода из одной структуры в другую". (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 66-69

In this article the author elaborates on his partial investigations (1999-2004) into the approaches of technique and methods of descriptions and the forecasts for development of social groups as sociological, economic and strategic problems. Transitional economic and managing processes are usual in the life of organized social groups; they are non-linear and contain conflict trends. We saw in our works a representative analogy for cycles of group life in math chaos and denoted the discrete model apriori as series of the attractors. Then modeling will aim at the seeking of signals of a series stage as attribute combinations: relative quantity of effective links and character of changing. But synergetic definitions for economics and for social studies are non-equal now. And researcher should does comparisons the digital metrics of economic models with attributive metrics of social processes correctly. The present-day social-economic phenomena might be considered as dynamic systems, but they have infinite complexity in a parametric model. We analyze the methodological aspects of investigator’s choice for simple effective discrete model in the complex social-economic medium as problems of calculation of the value (index) of complexity (topological, the dimension of system graphs). (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 70-71

A cake-cutting procedure is perfect if it satisfies the properties of efficiency, envy-freeness, and equitability. For two players there is no perfect procedure, including cut-and-choose and Austin's procedure. But the addition of money makes perfection possible, as we demonstrate by describing a 2-player, 1-cut perfect procedure that induces each player to be truthful in order to maximize the minimum portion of cake it can guarantee for itself.
For n > 2 players, an envy-free procedure can be rendered equitable with the addition of money, but not necessarily efficient if it uses more than n - 1 cuts (the minimal number). Although there is a minimal 3-player, 2-cut envy-free procedure, no 4-player, 3-cut envy-free procedure is known to exist. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 55-58

An investment project is a finite family of pairs {(ci, ti)}, where t0 <t1 <… <tn are the time moments and ci are the payments to the investor at the appropriate time moments. The investor has an opportunity of an alternative investment of means in bank which activity is characterized by continuous function of discounting f(t) non-negative and not growing at t³0 and such, that f (0 =1. Stability of financial conditions when the bank interest does not vary at time means that f (t) =vt where v <1 is a discount - factor. Some problems of optimization of parameters of the investment project with the given payments and an opportunity of a variation of the moments of payments are considered. We analyze Net Present Value and Profitability Index as parameters of investment project. The results are a base for the simple algorithms (linear or quadratic complexity) for solutions of these problems. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 71-74

Prognosis of original rhythmocascade algorithm of the society state based on non-linear dynamics and a society as a holistic system is under discussion. According to this approach some typical scenario of social progress development could be defined. The analysis of pre- and post- revolutionary situations in modern and middle age history of Russia is under the special interest. Differ from theoretical history approach the common tendency as well as dates are predictable. (full text)

Evolution of strategies in the Artificial Life model:
An Attempt of historical interpretation

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 74-78

Kinship is one of the major determinants of the social dynamics. Altruistic behavior toward relatives is an evolutionary stable strategy, but how can it change the overall dynamics of the social system? Computer simulations with the proposed model demonstrate that if conditions of local interactions and constrained resource capacity are held then kin-selection could dramatically change territoriality and level of internal warfare. In the social sciences the causes of destruction of kinship organization are conventionally considered as rooted in the fields of politics, economics, and religion. The results of the simulations indicate that a kinship organization can destruct itself without taking into consideration any of the aforementioned additional factors. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 78-80

To describe the processes of globalization the model of cooperation of two groups of the economical subjects is offered. The states can be considered as such economical subjects, between which there is a movement of financial assets. Using the given model and taking into account the economic information, it is shown, that the global financial market is not effective. (full text)

P.Ju. Chebotarev, V.I. Borzenko, Z.M. Lezina, I.V. Lezina, A.K. Loginov and Ja.Ju. Tsodikova

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 80-83

We propose and study a model of social dynamics governed by consecutive collective decisions. The decisions are made by means of the simple majority / qualified majority voting procedures. The current state of the system is characterized by the vector of actors’ welfare. At every stage, the body of voters can preserve status quo or accept a new external motion. The motion is a vector of actors’ welfare increments; it is generated stochastically. We investigate the impact of the collectivistic and individualistic attitudes on the social dynamics. Under rather weak requirements, the collectivistic behavior turns out to be more profitable than the individualistic one. On the other hand, if the environment is propitious and the qualitative majority threshold is high, the individualists’ welfare goes up faster. The interval of “high thresholds” is from about

to the value that gives rise to stagnation, where

is the share of the collectivistic group. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 84-85

В докладе обсуждаются особенности денег как информации, приведена модель взаимодействия валют. Показано, что это взаимодействие является антагонистическим. Рассмотрены различные сценарии возможного развития событий. Обсуждены условия реализации каждого из этих сценариев. (full text)

MATHEMATICAL MODELS AND METHODS
IN ANALYTICAL INFORMATIONAL SYSTEMS
FOR THE HIGHER AUTHORITY AND STATE STRUCTURES

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 86-88

There are a lot of mathematical models and methods used in analytical informational systems for the higher authority and state structures. I suggest scientific approach to the classification of the models and methods depending on the different data subjects. It has been carried out the description of the modern analytic and evaluated methods of the different social problems. (full text)

ON SOME MATHEMATICAL MODELS OF SOCIAL
RELATIONS IN HIERARCHICAL POWER STRUCTURES

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 88-90

This paper is devoted to researchers on mathematical modeling of “Power - Society” system built by A. P. Mikhailov. Now we tried to take into account some aspects, connected with social relations between the actors of power communications in hierarchical power structures. Three types of power structures have been taken under consideration: the political system of society on macro level, state power structure and modern organization on middle level. Clannish structures and patron – client relations have been examined. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 91-93

The paper considers reflexive mappings properties: it is proved that, when the agents in the framework of the game-theoretic model make their decisions on the base of the finite informational structures, actions, chosen by phantom agents, are defined by the system of nonlinear iterated mappings [1]. Exploration of the model allows concluding that the informational equilibrium is generally unstable under the increase of the reflexivity depth. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 93-95

We propose a method, which allows to realize the stabilization of chaotic dynamic in a simple micro-economical model. Our model consists of two firms competing on the same market of goods. The firms perform active and asymmetric investment strategies, i.e. their temporary investments depend on their relative positions on the market. Under certain parameter values the given model exhibits the properties of dynamical chaos consists of continuous power spectrum and positiveness of Lyapunov exponents. (full text)

MULTIPLE CRITERIA SYSTEMS OPTIMIZATION
UNDER UNCERTAINTY OF STOCHASTIC CHARACTERISTICS
OF NONDETERMINISTIC PARAMETERS

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 96-98

Multiple criteria decision making for systems with uncertain characteristics of nondeterministic parameters is considered. The general consideration is illustrated by some modification of portfolio selection problem. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 98-101

Scenario approach to bubbles description is introduced; its main ideas are stated. Some results are given. One of them is the procedure of an analysis of public and corporate debts to determine if these debts can be considered as bubbles. This procedure is used to investigate GKOs before 1998. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 101-104

We consider the “authority-society” model firstly introduced by A. P. Mikhailov. We introduce the generalized approach which supposes the existence of two stable authority profiles. The first profile is related to the hierarchy having a large number of powers, the second one – a small number of powers. We have shown that depending on the initial conditions and system parameters the authority profile at large values of time appears to be close to either one of these profiles or the so-called contrast profile. (full text)

DYNAMIC FEEDBACK STRATEGIES OF INVESTMENT MANAGEMENT
UNDER TRANSACTION COSTS AND PORTFOLIO CONSTRAINTS

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 105-107

The investment portfolio management problem with stochastic volatilities under trading volume constraints and proportional transaction costs is considered. The portfolio optimisation objective is formulated as a dynamic tracking task for some reference portfolio with desired yield. We propose to use the model predictive control methodology in order to obtain feedback strategies of investment portfolio optimisation. (full text)

CONNECTION OF THE RUSSIAN BANK RATES
WITH RATES OF ECONOMIC GROWTH AND INFLATION

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 108-110

The theoretical formula of connection of the nominal bank interest rate with the sum of rates of economic growth and inflation is offered. This formula is transformed in various econometric formulas which factors are estimated on monthly and annual Russian statistics for 1995-2001 j.j. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 111-114

The classification of ways, means and methods of financial risk management is considered. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp.115-117

The method of a calculation of the electoral cross-flow matrix. The elements of this matrix are estimations of the conditional probability of votinq for the j-candidate with a condition, that an voter is a supporter of i- candidate now. Values of electoral potantions are defined as extreme balance state of vector of electoral preferences. These values are received as the results of extreme transition for Chapmen-Kholmoqhorov equation. It has been offered several practical supplements based on the developed method. (full text)

Non-statistic method
for sociological data analysis
and the problem of rational opinion choice

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 117-120

The suggested method of automatic hypotheses generation uses the Facts Base (“respondent – opinion”) and generates opinions determinants along with the prediction of opinions choice. The generation is realized by plausible inference, which implements interaction of three forms of non-deductive procedures – induction, analogy and abduction. Being realized as an intelligent computer system, the method seems to be useful instrument for formalized qualitative analysis of sociological data in different problems of sociology and social psychology. The procedures (utilizing specially developed many-valued argumentation logic) for characterization of rationality of opinion choice are proposed. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 121-123

The problem of effective investment portfolios with the three criterions is considered. The correctness of the problem is considered. Existence conditions of the problem solution are obtained, and the method of numerical solution is investigated. (full text)

Alexey Andreev, Sergey Ljubkin, Alexey Rezer, Avner Ben-Yair and
Dimitri Golenko-Ginzburg

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 123-126

The backbone of our research is to create a new multi-parametrical optimization model in order to maximize the system’s utility as a generalized quality measure of the system’s functioning. Since such a model is, in essence, a trade-off compromise between the system’s parameters, we will henceforth call that model harmonization model. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 126-128

This paper considers discoalition game of two gamers with vector functions of outcomes and uncertainty. It being known only limits of uncertain characteristics. Vector functions of risk for every gamer is introduced according to principle of minimax regret. Guaranteed on outcomes and risks decision of this game is formalized. It has been found out “game” meaning of introduced decision, sufficient conditions of its existence and three properties: invariant concerning of affinities, condition of compactness of set of decisions and form of decisions of separate functions of outcomes. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 129-132

On the basis of the mathematical model describing the time dynamic of the information spreading, the problem of optimal control over external limited resources spending is set in order to maximize the number of people perceived the information. The model allows to study the character of growing informational influence, depending on the object's behavioural characteristic, and gives the possibility to find, using the methods of optimal control theory, the most advantageous solutions of such an influence on some social group. The optimal control problem is examined by analytical methods and the numerical solution is found. The numerical simulation is conducted on the basis of the model. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 132-136

While network auction is regarded as natural extension of ordinary "spot" auction it captures such crucial features as limited transportation capacity, cost of transportation and lost of commodity during transition. These features make it more sophisticated modeling issue. Yet present concern in regulation of gas and oil pipelines as well as wholesale electricity market renders network auctions study extremely up-to-date. We face now decentralizing trend in these markets with attempt to delegate governing role to competitive incentives. The mainstream of network auctions design study tries to implement double auction in network environment as self-regulating and information revealing mechanism. Using discrete supply or demand schedules for each node and leg of transport network and maximizing surplus via solving linear programming task ("smart auction") is the way that was primarily introduced and examined. Another approach implements dynamic double auction with induced orders and implies auto crossing-like real-time clearing. This mechanism also maximizes surplus but deals with continuous functions of demand and supply, which arise under certain assumptions about order making process. Dynamic approach allows even more decentralization and computational simplicity while giving exact values for both equilibrium node prices and leg flows comparing to exact flows but ambiguous prices in discrete schedules case. (full text)

Optimal Methods for Approximation of Reachable
Sets for Convex Dynamic Economic Systems

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp.

Optimal methods for approximation of reachable sets for dynamic economic systems are described. Convex systems with phase and mixed constraints are considered. Methods are based on polyhedral approximation of reachable sets for multi-step systems, which are convex in the case under consideration. Methods apply iterations, which include evaluation of support or/and distance functions. It is proved that the convergence rate of approximation is optimal with respect to iteration number and number of vertives/hyperfaces (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 136-138

Of all global problems world population growth is the most significant. The growth of the number of the people expresses the sum outcome of all economic, social and cultural activities that comprise human history. Demographic data in a concise and quantitative way describe this process in the past and present. Analyzing this development it is possible, by applying the concepts of system dynamics and synergetics, to work out a mathematical model for a phenomenological description of the global demographic process and project its trends into the future. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 138-140

It has been suggested a method of the indicator computing of the social phenomenon condition. The complex influence upon the social phenomenon condition is estimated with the aid of composite and individual indicators dependence. It has been established the functional dependence between composite indicator increment and the argument of the individual indicator increments. It has been developed the forming principle of the verbal-numerical evaluated scale. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 141-144

Our work is devoted to investigation of "multi" versions of antimatroids (dual of convex geometries). These discrete structures are present in many fields of mathematical social sciences. For instance, we can quote the theory of choice, where a first attempt to connect choice functions and closure operators appears in (Malishevski, 1994). Recently, this link was interpreted as duality between path-independent choice functions and convex geometries (Johnson, Dean, 2001), (Koshevoy, 1999), (Monjardet, Raderanirina, 2001). Another example is game theory where antimatroids are considered as permission structures for coalitions (Bilbao, 2003).
Multisets also arise in various areas of mathematics and computer science. The combination of notions of an antimatroid and a multiset, namely, an antimatroid with repetitions, was proposed by Bjorner, Lovasz and Shor in 1991 in order to analyze the chip game.
In this paper we define a poly-antimatroid as a family of multisets, and investigate the structure of quasi-concave functions on poly-antimatroids. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 145-145

SEQ CHAPTER \h \r 1A procedure for reaching agreement on multilateral treaties, based on “fallback bargaining,” is proposed. It identifies as a desirable compromise any point that minimizes the maximum Hamming distance to the top preferences of all players. This compromise may differ from the compromise produced by the usual procedure—voting on each treaty provision—which minimizes the sum of these distances. The proposed procedure is relatively invulnerable to strategizing, inducing players to be truthful in expressing their preferences, and has other important social choice properties.
The application of the procedure requires that issues be of more or less equal significance to countries and that they be as independent as possible. Applying the procedure to oil-pollution control negotiations among 32 countries in 1954 yields six compromise outcomes, all different from that produced by the usual procedure. Approval voting is suggested as a way to break ties among the compromise outcomes. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 146-148

To estimate the efficiency of national modern economy the model describing interaction of the enterprises, state and consumers of production, is offered. This model is described by a system of three differential equations. It was solved in the case, which is characterized by growth of financial resources concentrated in real sector of economy. The analysis of the results has shown that according to the model, the efficiency of the economy is determined by the ratio of the efficiency of the working capital and the capital flight. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp.148-151

A model of national economy describing financial flows between businesses, households, and the state is proposed. It is considered from the point of view of economics. Its pre-assumed conditions and the limits of its application are formulated. A clear economic sense is found for the model’s parameters and variables. A correspondence is established between them and statistical indices, which makes it possible to test the model on the empirical data. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 151-154

The mathematical reliability theory is not rather effective for systems functioning in vagueness conditions. That because it is necessary to work out new methods for such systems. We propose to use digraph as a system simulation. Every digraph vertex is in accord with system element and contains its reliability. We use impulse excitations as a simulation of vagueness conditions also. The impulse excitation decreases reliabilities of system elements. All these permit us to enter the comprehension of system stableness. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 154-154

For the first time a model of the regulated and open nonlinear three-sectors - economics is presented in this article. The author proved by means of the model that export of profits in case of fixed technological structure led to decrease of unindustrial consumption. On the contrary, raising of customs-duty on raw materials increases unindustrial consumption. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 155-157

The main of presented research is a demonstration of creating the society model on ethnic solidarity level. This model describes the behavior of ethnic system. The ethnic system includes a few ethnoses and provides their interactions. The interactions transmit by ethnic fields. The model is described by system of parabolic differential equations. The software TERRI is used for the forecast of arising the ethnic conflicts. Based on simulation result the researcher can compute the direction of ethnic field distribution and the most probable points of skirmish between ethnoses. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 157-163

The proposed model combines positive aspects of earlier models that have not been earlier combined within one model: it accounts for significant intercycle periods, on the other hand, through inclusion of the famine relief subsystem dynamics into the model it accounts for lengthy periods of very slow and unsteady population growth (when most part of the population had inadequate per capita acreage and there existed very strong incentives to innovate in the raising of the carrying capacity of land). Hence, this model could be used as a basis for development of a new generation of models accounting both for "secular cycles" and "millennial trends". (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 163-166

The mathematical model of economical interaction of two states is discussed. The market mechanism of production and prices formation is supposed. The modelling shows that "opened" economical systems are unstable. The social consequences of some variants of economical interaction are examined. (full text)

MODEL OF SPONTANEOUS SELFSTABILISATION VIA
AN UNSELECTIVE DEPRESSIVE EFFECT OF INSTABILITY
AND IT’S APPLICATIONS TO DIFFERENT ECONOMICAL PHENOMENA.

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 166-168

One presents a model of near bifurcation (

) dynamics in economy. An approximation in that

(

is an investment) &

(a price instability meager) are almost independent (when a system is strictly at (near and out of) the border of stability) is considered. In this case a new-type of resource boundaries (non-material) appear.

is considered as a resource and

in some way as a price. One analyses from this point a number of problems such as transitional phenomena, institutional catches, Illarionov’s paradox, Dutch disease, income inequality, unemployment, development inequality, insurance, inflation, taxes and different points of state control… (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 168-170

New method of analysis and forecasting of chaotic time series based on modified SSA scheme is offered here. As distinct from popular SSA scheme the suggested scheme takes into account non-steady factors, which affect investigated time series. Taking into account non-steady factors allows to improve the accuracy of forecasting. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 170-170

Strategic games are considered where the players participate in certain `activities. Each activity generates a `level of satisfaction,’ shared by all participating players. The utility of each player is an aggregate of the relevant levels. Attention is paid to the aggregation functions ensuring the acyclicity of individual or coalition improvements regardless of other characteristics of the game. In particular, special roles of additive aggregation, as well as of the minimum/maximum ones, are demonstrated. (full text)

ASYMPTOTIC SOLUTION OF DISCRETE PERIODIC
SINGULARLY PERTURBED OPTIMAL CONTROL PROBLEM

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 171-174

The asymptotic expansion of the solution of a nonlinear discrete periodic singularly perturbed optimal control problem is constructed as series of non-negative integer powers of a small parameter. The estimates are obtained for the closeness of the approximate solutions to the exact one and it is proved that the values of the minimized functional do not increase when higher-order approximations to the optimal control are used. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 174-177

Four Russian socio-economical crisis since 1995 are under this investigation. Combination of two stock market indexes AKM and DJI can predict 3 of 4 this crisis. (full text)

MATHEMATICAL MODEL OF SOCIETAL COMMUNITY, SYSTEM OF
MAINTENANCE OF INSTITUTIONAL ETHNIC SAMPLES, POLITICAL
AND ECONOMIC SYSTEMS BASED UPON THE IDEAS OF T.PARSONS'
THEORY OF SOCIAL ACTION

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 177-179

We are constructing the model using a system of four differential equations, which describe the following subsystems of the social system. After the construction is completed, we analyze the system analytically, and model it on the computer. The constructed and analyzed system agrees well with the theory offered by sociologists. (full text)

ON A PROBLEM OF NONLINEAR DYNAMICS IN THE FORM
OF PARABOLIC EQUATION WITH NO LOCAL SOURCE TERM

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 179-181

Among many problems of nonlinear dynamics we often see heat equation with nonlinear source term. In this talk we consider such an equations with nonlocal term in

. We find conditions on the parameters for which this problem has only local in time solutions, in other words the problem has so called blow-up phenomena. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 182-184

The problem of evaluating Web pages quality is solved by means of self-consistent choice approach borrowed from voting theory. This method needs no damping factor to rank Web pages. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 184-188

A stochastic network project of PERT type is considered. The duration of each activity is random and the corresponding probability density function is pregiven. Each activity consumes several renewable resources of different types with fixed capacities. The resources are at the disposal of the project management and are in limited supply for each type of resources. The resource limit is independent on time, i.e., is fixed at the same level throughout the project's duration. Since each activity entering the project is of random duration, the corresponding feeding-in resource moment to be determined is a random value too. The problem is to determine the random starting time moments for each activity subject to resource constrained limits in order to minimize the average project's duration. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 188-191

The work concerns mathematical modeling of resource consuming. The model of oscillations of livestock in Kenya was elaborated. The model investigates the origins of ecological catastrophes. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 191-194

The report devote to investigation of such actual modern problems as globalization and sustainable development. Growth of intercommunications between different world regions and tendency to increase of capital movement freedom and labor force signify that world may be regarded as uniform system in construction of mathematical models. Therefore sufficiently simple global models of strategic character bring to the forefront. As example of these models it is regarded Forrester's model which was the first global model. Using this model it is investigated concept "sustainable development", which is interpreted as stabilization of world system basic material characteristics. It is shown how may be guaranteed an achievement of sustainable development of Forrester's model world system by means of certain arrangements. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 195-198

In this report we propose a view on history as applied science. We to draw attention to interdisciplinary approaches and methods of nonlinear dynamics in historical studies. We discuss the development of theoretical history proposed a decade ago. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 198-201

The problems of mathematical modelling of historical processes are discussed. Main attention is attracted to modelling of selforganization and evolution of social systems. The general principles of historical model building are discussed. Some models of historical dynamics are presented. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 201-204

The problems of spatial historical dynamics are concerned. We propose a system of mathematical spatial models describing different aspects of global historical process. Economics, trade, demography, politics, wars and migrations are taken into account. Some problems having both subjective and instrumental nature are analyzed and discussed. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 204-209

In this paper, a method for the determination of the trend for a time series is presented. A comparative study was made between the seasonal components and the aleatory components, which were computed by this algorithm and these founded by an additive model. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 209-212

At a meeting with the leadership of the Russian Academy of Sciences on December 3, 2001, Russian President V.V. Putin set two objectives before the scientific community. The first one is to search for scientifically justify ways of transforming the country’s economy from its present raw-material orientation to an innovative way of development; the second is to scrutinize government decisions and forecast and prevent disasters, catastrophes, and instabilities in the anthropogenic, social, and natural spheres. The first of these tasks is about evaluating the corridor of Russia’s opportunities and choosing a historical perspective; the second involves parrying threats, protecting the country from dangers, and preventing disasters along the historical way that society will choose after solving the objective. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 212-217

It is shown that concurrency

and labor consuming

of any good elaborated in new production are connected by linear law

. Negativity of the parameter

means that high labor consuming productions are not concurrent in inner and outer markets. It is proved that

, where

are local and world taxes on raw materials, mainly on oil and gas,

are local an world taxes on ordinary productive activity. Custom taxes and transport expenses perturbs the linearity but common tendency retains. That points a way how to turn an economic orientation from raw production to world workshop. (full text)

TOWARDS APPLICATION OF NATURAL SCIENCES
MODELS TO PROBLEMS OF GENERAL POLITOLOGY

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 217-217

It is impossible to imagine contemporary science, technology and many other fields of creative activity apart from mathematical modeling. Due to its universality, flexibility and accuracy this methodology won a lot of fields of knowledge from technical systems design and control to analysis of social and political processes. Although nobody can await from mathematical modeling of social life the accuracy and predictability of modeling in natural sciences and in technology, under some conditions the modeling of these supercomplex phenomena may be performed successfully. For this it is necessary to combine efforts of various specialists around some actual problem. One of these problem is relations in the system “Power-Society”. In this paper we represent mathematical model of this system and results of modeling with respect to some important macro-political events in history of Russia in XX-th century. (full text)

МОДЕЛИРОВАНИЕ ЛАТЕНТНЫХ ИЗМЕНЕНИЙ
С ПОМОЩЬЮ СТУКРТУРНЫХ УРАВНЕНИЙ

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 217-220

Latent Growth Modeling allow to study dynamical process in social and humanitarian science. Along with sequential path analysis of repeating measurments of one variable or several ones, which can form associative model or latent factor’s model LGM is a powerful and flexible techniques which allow to study changes in inter- and intra-individual levels. Each of these methods has it unique benefits and limitations. In this paper, we will demonstrate several of them, contrast and apply to analysis of real data from behavior science. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 221-223

Dynamic system consists of several constantly revived projects that are swap transactions on world mixed market. We consider a multistage conversion scheduling as a project realization yielding a premium. An institutional investor has a set of resources, which he invests in projects for a deriving a premium. All projects can be executed at the same time, but the implementation each of them needs different resources. An investment procedure completes by realizations of all projects. Maximal independent nodes set of a constructed graph accords to maximal number of simultaneously projects implementation. Dynamical investment distribution model is suggested in the report too. (full text)

MATHEMATICAL METHODS AND PEDAGOGICAL APPROACHES
OF ECONOMIC THINKING DEVELOPMENT OF TECHNICAL
INSTITUTE STUDENTS

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 237-240

Current reality makes us treat a new system of education in a quite different way. There is a necessity to develop economic thinking of children, beginning from any age. And we study the development of economic thinking of Technical Institute Students. (full text)

GAME THEORETIC FORMALIZATION OF THE HIERARCHICAL
CONTROL OF SUSTAINABLE DEVELOPMENT

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 240-242

A conception of the hierarchical control of sustainable development based on game theoretic modeling is proposed. The principles of optimality of the hierarchical control of sustainable development as solution sets of the hierarchical game theoretic model are formulated. The organizational and ecological-economic interpretations are discussed. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 242-245

The traditional approach to measuring the hierarchical status in organizations [1-4] treats the status as a one-valued function of the organizational structure. This approach ignores the real dependence of the status value on the social stratification. A proposed new measure function of the hierarchical status takes into account both the organizational structure and an organizational stratification by criteria of sex, age, nationality, and so on. Some formal properties of the measure function are analyzed. A case study using the program implementation of the proposed model is discussed. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 245-245

We define two versions of stability and efficiency of partitions and analyze their relationships for some matching rules. The stability and efficiency of a partition depends on the matching rule. The results are stated under various membership property rights axioms. It is shown that in a world where agents can freely exit from and enter coalitions, whenever the matching rule is individually rational and Pareto optimal, the set of stable and efficient partitions coincide and it is unique: the grand coalition. Then we define a weaker version of stability and efficiency, namely specific to a given preference profile and find some negative results for stable matching rules. (full text)

РАЗРАБОТКА МЕТОДОЛОГИИ СОЗДАНИЯ ТОРГОВОЙ СИСТЕМЫ
ДЛЯ РОССИЙСКОГО РЫНКА ЦЕННЫХ БУМАГ НА ОСНОВЕ
ТЕХНИЧЕСКОГО АНАЛИЗА И ЕЕ ОПТИМИЗАЦИЯ

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 246-249

There are some theoretical foundations of technical analysis, which are considered in this work. The trading system, which generates signals to buy and sell securities, is based on mathematical method of technical analysis. While making investment decisions at securities market the system of indicators is the subject of research. Shares of the Russian issuer, such as RAO UES, Lukoil, Rostelekom and Surgutneftegaz are regarded as the subject of research. Moden techical analysis computer programs applications were used in this research (Metastock7.0 Professional and Omega Research Prosuite). (full text)

TECHNOLOGIES UNIFYING MATHEMATICAL AND
HUMANITARIEN METHODS OF ANALYSIS AND PROGNOSIS

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 249-252

The simple processes, systems, phenomena are studied and forecasted by mathematical methods. Complicated processes, systems, phenomena are studied and forecasted by humanitarian methods. The frontier between simple and complicated processes and correspondingly mathematical and humanities methods of prognosis is not fixed and not too accurate. Development of mathematical modeling technologies leads to invasion into not yet explored fields. Opposite process occur: it is necessary “to understand” phenomena, which is subjected to mathematical modeling. Therefore interaction between mathematical and humanities methods have place. Result are forming technologies of analysis and prognosis unifying mathematical and humanitarian methods. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 252-254

В докладе рассматриваются принципы принятия решений в условиях изменяющихся внешних условий, изложена соответствующая математическая модель. Показано, что в зависимости от характера внешних изменений среды целесообразны различные стратегии поведения, обеспечивающие минимизацию возникающих издержек. На основе полученных результатов предложено объяснение различия западной "философии активности" и восточной "философии недеяния". (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 255-258

Ethnopolitical conflicts are an extremely important problem of the modern Russian Federation, whose population consists of about 150 different ethnic groups. The example of Chechnya showed the world the extent to which such a conflict can evolve. The North Caucasus is one of the most politically active, conflict-ridden areas in the world. Mathematical methods were applied to examine conflict behavior in order to provide a clear picture of the situation and to analyze ways of alleviating the problem. There were some urgent questions that can be answered with the help of detailed econometrics analysis of available data. Results are presented in this paper together with some possible explanations of observed patterns. (full text)

REGIME OF LOSSES FROM NATURAL DISASTERS IN
CONNECTION WITH CHARACTERISTICS OF SOCIETY

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 259-261

The amount of losses from natural disasters rapidly increases with time. Being extrapolated in the future this loss values in a few decades will approach the values of the annual economic growth of the world economics eliminating this way the very possibility of the economic development. However, the alternative interpretation of the regime of loss values from natural disasters can be presented. This model and the connection of the regime of losses from natural disasters with social and economical characteristics of society are discussed. (full text)

FORECAST OF GRADUATE PUPILS OUTFLOWS ON ASSESSMENT
TO EDUCATIONAL INSTITUTIONS IN VARIOUS UNITS OF RUSSIA
FOR THE MIDDLE-TERM PERSPECTIVE (2015)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 261-263

Influence of graduate pupils outflow on enrollment to primary, secondary and high educational institutions is forecasted for all 89 Russian units. School-leavers outflow to regional centers, particularly, Saint Petersburg and Moscow is taken into consideration. Graduate pupils outflows during the last years are scrutinized. A discrete dynamic model on graduate pupils outflows to primary, secondary and high educational institutions is built up. (full text)

SIMULATION DEVELOPING AND FORECASTS ON THE TURN OVER
OF A TEACHING STUFF IN HIGH EDUCATIONAL INSTITUTIONS

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 264-266

Stuff turn over in professional educational institutions is getting more and more topical. Mathematic model of the teaching stuff turn over inside an institution is being developed. Data on the age groups in Petrozavodsk State University for 1998-2002 are given as an example. 5 group ages from 23 years old till 70 years old are overhauled. Interpolation of an extended data is done by means of cubic spline at compound conditions. A discrete dynamic model in the form of difference linear equation system is a basis of the mathematic model. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 267-268

The reasons why any electoral system distort the voters’ preferences are discussed. Several well-known disproportionality indices for proportional representation systems are analyzed. Two new disproportionality indices are introduced and calculated for parliaments in several countries. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 269-272

Life-consuming technologies concept based approach to the global demographic process is proposed. The phenomena of population growth and demographic transition are explained and the maximum world population is estimated. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 272-275

The main problem of approximation for a function is choice of empirical formula. In this work a particular class of the monotonous two-parametric functions

is considered for solution of this problem. These functions are pooled to form one class by a common property concerning so-called generalized average. The main advantage of proposed approach is that proposed set of the empirical functions is not accidental but logically justified. It makes it possible to carry out graphical express-analysis of the studied dependences without complicated computations and take into account not only statistical but also analytical information on an economic phenomenon under study. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 275-277

In this work we consider the questions of management for production output on example of one of omsk’s enterprises, concerning with production of the disposable plastic dishes of the broad assortment. The Problem of production management is reduced to determination of such plan of production that total profit from sales of products of each type is maximum, but operation of production reconstruction together with starting-up and adjustment takes minimum time. We have define such mathematical models of the process, solving which, it is possible to determine the optimum plan of production of each type output under specified conditions. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 277-279

The model is suggested that describes the situation of ideas competition under the circumstances of political environment composed of two groups. One group is formed by politically active people who potentially may become supporters of one of competing ideas. The other group is formed by people politically indifferent at the moment under consideration. In general case people may move from one group to another. The ideas compete to attract the maximum number of supporters from politically active group of people. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 279-283

We discuss two-person nonzero-sum games which are generalizations of traditional duels. We describe equilibrium situations for duels of various types (discrete, continuous and mixed). Conditions for Pareto optimal play to be achieved in the equilibrium situation are given. Sufficient conditions for quasi-antagonisticity are found. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 284-289

The classic model of general intertemporal equilibrium is presented as dynamic system for financial values. There exits the first integral of optimal trajectory of each agent which may be interpreted as the own capital of the agent. The new description of ideal equilibrium may be used as phenomenological base for modeling non ideal economic systems. This result together with the results of analysis of structure of previously built successful model gives the way to the new technology of modeling. (full text)

TECHNOLOGY OF BUILDING MACROMODELS OF INTERTEMPORARY
EQUILIBRIUM WITH THE HELP OF THE INTELLECTUAL TOOL ECOMOD

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 289-293

The ECOMOD system supports the proper structure of an agent-based macroeconomic model taking into account the natural ambiguity of economic concepts. The system is based on the classification of model relationships and variables which expresses their meaning and supports a) editing relationships; b) syntax control; c) semantic control; d) control of balances of assets; e) dimensionality control (existence of consistent system of measurement units). The technology of modelling provides usage of the universal system of analytical conversions for solution of optimization problems circumscribing behaviour of the agents. The perspectives of development of the means remembering a previous history of each analytically transformed interrelation are discussed. The work is done - with the financial support of the Russian foundation for basic research (project code 04-01-00606) - according to program of State support of leading scientific schools (project code НШ-1843.2003.1). (full text)

THE APPROACH TO THE DESCRIPTION OF MAECENAS INFLUENCE
ON ECONOMIC RESULTS OF A BENEFICENT COMPANY

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 294-296

The economic decisions of the beneficent company now gets the special importance, as it will allow to develop the concept of charity. The strategy of charity can be developed after the model of interaction between beneficent company, recipient of grant and the state, as regulating system, will be created. To describe the influence of charity on the Maecenas business activity it is offered to use some disturbing function. This limited in time function increases the investment appeal of the beneficent company. The income dynamics of the beneficent company can be described by the system of differential equations. The solution of these equations allows to make a proposal of charity strategy. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 296-298

The necessary and sufficient conditions of total conditionally of system (1) (below) are obtained. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 298-303

The behaviour of the society is considered like a Carno cycle. Considered variables are enthropy and temperature. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 303-303

It is shown how it is possible to assess the range of the social interactions between households from migration data. It turns out that the occurrence of "white flight" becomes important at distances of about 100 meters per household. From that observation one can derive the strength and range of the interactions between households. (full text)

INFLUENCE OF EQUIPROBABLE DEFLECTIONS OF MARKET
ON STATISTICAL RESULTS OF TRADE SYSTEMS

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 303-306

The fluctuations of prices on exchange market with determined by share of confidence possible to consider equiprobable. However rules of completion of deals such a that exist the certained slantings of results of trade systems, regardless of that, what algorithm they use. However, resting only in suggestion about that that deflections of the prices in one or another side are equiprobable, possible forecasts of statistical results of functioning of the trade systems. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 307-307

In social choice theory, aggregation of individual preferences can be performed using a variety of competing methods, including so-called "scoring rules". Depending on the model for representation, as well as on the method for aggregation of individual preferences, one can arrive on different conclusions about group preferences given the same original data. Even within a fixed preference representation model and aggregation rule, group preference relations derived from a random sample may or may not reflect "true" population preferences. Tsetlin & Regenwetter(2003) showed how probabilities of obtaining correct/incorrect majority preference relations from a random sample can be evaluated using sampling and Bayesian frameworks. We extend their approach by applying the same framework to a variety of other (positional) scoring rules, using generalized definitions of those rules for preferences represented in terms of mixed probabilities. We use realistic distributions to access empirical probabilities of "correct" or "incorrect" group outcomes from the various national election survey data. We discuss how these probabilities and confidence bounds on them depend on the sample size, preference representation model, and scoring rule. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 308-310

Complicated demographic situation in Russia is characterized by the negative rate of natural increase (RNI) which is not compensated by positive net migration. Thus, the total population size decreases leading to numerous socio-economical problems, in particular to the labour market problem. As in the middle-term perspective significant fertility increase is not expected, migration increase may be considered as a solution of depopulation problem. Thus, a question concerning migration streams which ensure population non-decrease (so called replacement migration) is raised. Within the framework of Leslie matrix model of population reproduction a problem of regulation replacement migration is considered. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 311-311

A procedure for electing committees, called the minimax procedure, is described. While based on approval voting (AV), it chooses the committee that minimizes the maximum “Hamming distance” to all voters (minimax outcome). Such an outcome may be diametrically opposed to the usual AV outcome, which minimizes the sum of the Hamming distances to all voters (minisum outcome). Computer simulation is used to determine how much, on average, minimax and minisum outcomes diverge. The manipulability and monotonicity of the minimax procedure are also investigated. The minimax procedure is applied to the 2003 Game Theory Society (GTS) election of a council of 12 new members from a list of 24 candidates. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 311-314

We study the dichotomous choice model, which goes back more than two centuries ago, as far as [4]. A committee faces two alternatives, of which only one is correct, and decides by the simple majority rule. Condorcet's statement may be phrased as composed of the three parts: A group decision, utilizing the simple majority rule, is more likely to be correct than that of any of the members. The advantage of a group decision increases with the size of the decision body. The probability of the group to make a correct choice using the simple majority rule tends to 1 as the number of members tends to infinity. Condoret's Jury Theorem has been a subject of extensive study for several decades. It provides a theoretical basis of public choice theory and political science theory (cf. [7]). Here we focus on the second part of Condorcet's statement, in particular on the question if a small augmentation of the committee is always an advantage. The answer depends on the interpretation. For a fixed committee and random subcommittees it is unconditionally correct (see [1], [2]). However, this is not necessarily the case in general. (full text)

RESULTS OF SIMULATION OF CONSTITUTING PRINCIPLES OF LIVE
AND OF LIVING ACTIVITIES IN RUSSLANDIAN FEDERATION
(IN BROADER SENSE, IN NORTHERN EURASIA)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 314-320

This article tries to explicitly look at the state, business “society”, religious “societies”, cultural and scientific “societies” etc. as multi-agents (of high hierarchical organizational level) that do live in certain environment. This allows not only to analyze the existing relations between different kinds of multi-agents, but also to try to positively influence or construct conditions for optimizing the relations between these agents with the scope to adequate these relationships to the specific kind of environment. The “philosophical” point of view of this article also permits to build the general goal function for the co-evolution of multi-agents (of high hierarchical organizational level) in their environments. This article is written using the modern northern-american literature to the complex adaptive systems (see references) and is the basis for the modeling work in the Foundation for Monitoring and Forecasting of Developments in Cultural-Territorial Spaces (www.fmprktp.org). (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 320-321

The aim of this work is to analyze the dependence structure between losses and expenses in excess-of-loss reinsurance. In our investigations we used the extreme value copulas and proposed a new asymmetric logistic model of extreme dependence function. Our results could be useful in evaluation of reinsurance premiums. The relevance of our approach was provided by intensive computer mofeling. (full text)

mathematical view on the difference between
"Western" and "oriental" agrarian societies

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 322-324

Mathematical model describes typical processes of production, redistribution and consumption of material welfare in agrarian society, taking account of geoclimatic conditions in Europe and Asia. It is shown that geoclimatic factor causes differences in social structure. (full text)

Mathematical modeling in structure of displaying
of political object: limits of opportunities

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 325-329

Mathematical modeling is the most important means of display of objects in a politics. Its using is justified and effective when verbal display becomes insufficient because of big number of parameters or necessities of the quantitative description. In a politics the requirement for mathematical model is especially actual in connection with impossibility of research experiment on real political object. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 329-329

In article the corruption hierarchy which is a part of the qovernment hierarchy studied in works by A.P.Mihajlov is investigated. The basic postulate of behaviour of the corrupt official is formulated. On his its basis the mathematical model of corruption hierarchy is constructed. Various scripts of development of mutual relations of corrupt bureaucracy and the state are investigated. (full text)

FIRM ADAPTATION MANAGEMENT ALGORHYTHMS UPON
THE CHANGE OF THE SITUATION IN THE MARKET

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 329-332

The problem of firm parameters optimal means according to its adaptation to market conditions is solved. The evaluation task of adaptation efficiency depending on expenditure guantity of firm parameter change – investments, on the example of food industry enterprises is also solved. (full text)

CONSEQUNTIONS OF INCLUDED SUBGROUPS AND MODELING
OF EVOLUTION ANCIENT SOCIETY (RESULTS OF PARALLEL
CALCULATION AND ITS INTERPRETATIONS)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 332-334

In this report results of parallel calculations (look at Appendix) for great group gratings for Sn (n³4) are discussed. The model of very old society are presented on the path on group grating. Especially we are interesting in those tracks, which may be considered as, in a sense, minimum path. Finally, some problems which could be described in terms of changes low H(n) = LnL + (n-1)Ln(n) - LnLn(n-1) - n (by W.M.Bechterev) are discussed. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 335-337

A new approach to research of differential equations with aftereffect is considered in the report. Modifications of some well-known models micro- and macroeconomics are suggested. Effective sufficient stability tests of such models are demonsrated. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 337-340

In 1973–75 Gibbard and Satterthwaite published a fundamental impossibility theorem which states that every non-dictatorial social choice function, whose range contains at least three alternatives, at certain profiles can be manipulated by a single individual. After that, the natural question arose: if there are no perfect rules, which ones are the best, i.e. least manipulable? The answer to this question cannot be given in absolute terms. It stipulates introducing a certain index of manipulability of the rule and a certain model for the population. The answer may depend both on the choice of the index and on the choice of the model. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 341-343

The article substantiates a new approach to the choice of tax schedules based on several mathematical models. The first model, based on game theory, helps to construct the average tax rates schedule. The second is an optimization model used to construct the marginal tax rates schedule. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 343-346

Many economical systems are distributed, the most simple example of distributed economical system is illustrated by Beckman’s transportation flow model kf / |f| = grad l, where l is good’s price, k is transportation tariff and f is local transportation flow. We can also illustrate distributed economic systems by Black — Sholes’s derivative instrument pricing model in financial theory, generalized Tiele’s model in insurance theory, etc. The necessary conditions for optimal control of such systems satisfying partial differential equations are formulated as Lagrange — Pontryagin’s maximum principle generalization. The economical and financial applications are discussed. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 346-349

In the standard framework of the macroeconomic model with a representative consumer, producer and government we suggest a definition and a description of structure of the society losses from policy steps of the government. A theorem asserts that the society surplus is added of the consumer’s, producer’s, and the government’s surpluses. In particular, the theorem generalizes the Bailey’s (1956) classical result on costs of inflation. The work contains also some results of comparative statics, and a calculation experiment with a model calibrated on Russian data. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 349-352

On the basis of the minimal covers, it is introduced the variation index

which extends the applicability of fractal analysis to study of various natural, technological and social chaotic processes. In particular, for the case of financial series, it is shown that the minimal scale

which is necessary for determining

with an acceptable accuracy, is two orders smaller than the one for computing the Hurst index H. This allows us to consider

as a local fractal characteristic and to show that

is related to the stability of underlying processes. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 352-355

When analyzing the situation in Russian secondary school. it seems necessary to forecast the developing tendencies in education under particular social-economical conditions? and one of the main features here is the age structure of teachers employed.
This forecast can be made with the help of the proposed mathematical model, including mail factors that influence the age structure of teachers. The model is built, considering the main differences between work forces of secondary school and ones of high school.
The definite parameters of the model can be obtained from the results of social and statistical studies. The parameters being defined, it is possible to make forecasts of age structure dynamics and of general social situation in secondary school under different social-economic scenarios in the country. (full text)

THE REDUCTION TECHNIQUES TO TIME-OPTIMAL CONTROL PROBLEMS
FOR NON-LINEAR SINGULARLY PERTURBED SYSTEMS

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 356-358

Time-optimal control problems for systems with fast (singularly perturbed) and slow motions are under consideration. There are obtained sufficient conditions for the value function, which is equal to minimal time of arrival to the given target set, to converge as speeds of fast variables tend to infinity. The researches are based on the coincidence of the value function and the unique lower semi-continuous minimax solution to a Dirichlet problem for the Bellman equation. The suggested construction of the limit value function can be considered as a development of the reduction technique. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 358-362

The approach is based on the interpretation of Pliska and Belecky [1],[2] continuous time portfolio optimization model. This model takes into account the fact that the mean return of individual securities or asset categories are explicitly affected by underlying economic factors as dividend yield, a firm’s return on equity, interest rates, unemployment rates, etc. Methods of risk sensitive control theory are employed, using an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance and a single risk aversion parameter. Our approach allows to align interests of managers and investors in the following sense: we find the optimal strategy of the full capital distribution between the managers fee and investors, maximizing the expected growth rate of capital on big enough interval of time, taking into account a manager’s skill to raise the capital of the fond in the risk averse case. Thus it becomes clear, in what situation (at what parameters of activity) the manager should be remunerated and in what sizes and when it is fined and on how many. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 363-365

Social processes forecasting has become more urgent and demanded in modern society. It is usually inconvenient to apply traditional methods to solve the problem, several reasons taken into consideration. In this connection it is recommended to use a comparatively new approach, based on Learning Genetic Algorithm for Prognosis (LGAP). Numerous experiments proved that high degree forecasting can be achieved with the use of the method. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 365-367

A normal form game of coalition formation is presented in which each player's strategy is a list of coalitions she is willing to form. This is an enrichment of the strategies spaces that have been proposed in the literature. Indeed, in the normal form games proposed by Von Neumann and Morgenstern (1944) and Hart and Kurz (83) one player's strategy is to choose the coalition to which she wants to belong. However, "a priori", when a player is willing to negotiate, she knows that she is willing to form different possible coalitions, even if her objective is to reach the best choice available. Hence, for a given strategy profile, the feasible coalitions are coalitions such that they are in the list-strategy of each member. For each strategy profile, we define the feasible set of coalitions and for each individual, her individual feasible set consists of those elements of the feasible set to which she belongs. In general, the coalitions in a feasible set do not form a partition of the set of players. (full text)

ON THE POSSIBLE REASONS FOR THE HYPEREXPONENTIAL GROWTH OF THE EARTH POPULATION

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 367-369

A new model of the Earth population growth is offered. It shows that the hyperbolic growth presents the transition period between zero growth (after filling its own ecological niche) to the exponential one. The difficult problem of explaining the hyperbolic growth in the XVIII-XX cc. is discussed. (full text)

SECULAR CYCLES: LONG-TERM OSCILLATIONS IN ECONOMIC
AND SOCIAL STRUCTURES OF AGRARIAN SOCIETIES

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 370-373

One particularly interesting dynamic pattern in history is the oscillation of centralization and decentralization of political power, seemingly affecting all hierarchical macrosystems, from systems of chiefdoms to world empires. What sociopolitical mechanisms may explain these dynamics? I will present some mathematical models and data that address this question. (full text)

CONCEPT OF TIME-EVENT CONTROLLED PROCESSES — A WAY TO THE MOST
GENERAL FORMULATIONS OF PRODUCTION PLANNING AND REGULATION PROBLEMS

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 373-376

A proposed approach to production planning or regulation problems formulation explicitly takes into consideration the fact that the qualitative state of a production system changes after some events, so instants of these events are treated as ends of plan period stages. To find instants of events of a certain type corresponding relationships are introduced into the model. The general formulation of the new models class is given. These models give the possibility to apply exact optimization techniques for determination of values of some parameters that earlier might be appointed only by experts and to embrace in a sole problem statement a lot of plan problem variants that traditionally may be regarded only separately. Such kind of models may be treated either as deterministic or stochastic that lead to broad possibilities of controlled processing modeling in the context of planning as well as the programmed processed regulation due to various disturbances. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 376-378

Creation of the efficient tax system is one of the most important tasks for countries in transition. The present paper aims to discuss the main components of this complicated problem. The first one is the choice of the tax structure and tax rates in order to get the desirable tax revenue. The second problem under consideration is determination of the optimal tax schedule and audit strategy for direct taxes. The paper also discussed several issues related to tax inspection organization and creation incentives for the efficient work of inspectors. Models of interaction between taxpayers and inspectors take into account corruption, audit costs and random mistakes of participants. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 378-382

The modification of system Lotka - Volterra considered. The modification enables to take into account natural unpredictable influences on ecosystem. The algebraic models, allowing to describe are investigated also dynamics of system to within the description of a variable state. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 382-385

In this paper a dynamic model of a state and more generally of a nomós (i.e. a linked vitally active community) is introduced (see also [1]). The vital activity of a nomos is presented in the form of a vitally organizing cycle of streams of results of substantiating, directing, and ensuring activities, linking units and main parts of the nomos with each other and also with the natural environment and the external organized environment. The model describes only a nomos with a constant construction. (full text)

APPLICATION OF SYSTEM DYNAMICS FOR MODELING FIRM
FUNCTIONING AND ESTIMATING OF ITS ACTIVITY UNDER UNCERTAINTIES

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 385-388

Nonlinear dynamic mathematic model of a firm is build using approach of system dynamics. The problem of firm activity estimating is solved for purposes of further firm optimization and control. This is the problem of model state and parameters estimation under conditions of imperfect and incomplete data. (full text)

Proceedings of the International Conference "Mathematical Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004, Moscow, Russia. - Moscow, RSSU,2004. pp. 388-388

Noncooperative game under uncertaity is considered. Each payoff function is accomplished by risk function. Properties of this extended game are investigated. (full text)