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Of all publications in the section: 24
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Article
Яновская Е. Б. Математическая теория игр и ее приложения. 2012. Т. 4. № 2. С. 96-123.

Most of solutions for cooperative games with transferable utilities (TU) are covariant with respect to positive linear transformations of individual utilities. However, this property does not take into account interpersonal comparisons of players' payoffs. The constrained egalitarian solution defined by Dutta and Ray  for the class of convex TU games, being not covariant, served as a pretext to studying non-covariant solutions. In the paper a weakening of covariance is given in such a manner that, together with some other properties, it characterizes only two solutions -- the prenucleolus and the Dutta--Ray solution -- on the class convex TU TU games.

Added: Mar 20, 2014
Article
Молчанов П. С., Ущев Ф. А. Математическая теория игр и ее приложения. 2013. Т. 5. № 3. С. 27-57.
Added: Nov 18, 2013
Article
Смирнова Н. В., Тарашнина С. И. Математическая теория игр и ее приложения. 2012. Т. 4. № 1. С. 55-73.

In the paper we consider a new solution concept of a cooperative TU-game called the [0,1]-nucleolus. It is based on the  ideas of the SM-nucleolus, the modiclus and the prenucleolus. The [0,1]-nucleolus takes into account both the constructive power v(S) and the blocking power v*(S) of coalition S  with coefficients alpha and 1-alpha, accordingly, with alpha\in[0,1]. The geometrical structure of the [0,1]-nucleolus is investigated. We prove the solution consists of a finite number  of sequentally connected segments in R^{n}. The [0,1]-nucleolus is represented by the unique point for the class of constant-sum games.

 

Added: Oct 11, 2015
Article
Крепс В. Л., Доманский В. К. Математическая теория игр и ее приложения. 2014. Т. 6. № 3. С. 32-53.
Added: Oct 23, 2015
Article
Яновская Е. Б. Математическая теория игр и ее приложения. 2010. Т. 2. № 3. С. 106-136.

Cooperative games with a restricted cooperation, defined by an arbitrary collection of feasible coalitions are considered. For this class the Equal Split-Off Set (ESOS)is defined by the same way as for cooperative games with transferable utilities (TU). For the subclass of these games with non-empty cores the Lorenz-maximal solution is also defined by the same way as for TU games. It is shown that if the ESOS of a game with a restricted cooperation intersects with its core, then it is single-valued and Lorenz dominates other vectors from the core, i.e. it coincides with the Lorenz-maximal solution. Cooperative games with coalitional structure for which the collection of feasible coalitions consists of the coalitions of partition, their unions, and subcoalitions of the coalitions of the partition, are investigated more in detail. For these games the convexity property is defined, and for convex games with coalitional structure existence theorems for two egalitarian solutions -- Lorenz maximal and Lorenz-Kamijo maximal -- are proved. Axiomatic characterizations for both these solutions are given.

Added: Mar 20, 2014
Article
Крепс В. Л. Математическая теория игр и ее приложения. 2017. Т. 9. № 3. С. 3-35.

With the help of a simplified model of multistage bidding with asymmetrically informed agents De Meyer and Saley demonstrate an idea of endogenous origin of Brownian component in the evolution of prices on stock markets: random price fluctuations may originate from strategic randomization of "insiders". The model is reduced to a repeated game with incomplete information. The present paper contains a survey of multiple researches inspired by this pioneering paper.

Added: Oct 17, 2017
Article
Петросян О. Л. Математическая теория игр и ее приложения. 2015. Т. 7. № 2. С. 49-68.
Added: Nov 24, 2017
Article
Антощенкова И. В., Быкадоров И. А. Математическая теория игр и ее приложения. 2014. Т. 6. № 2. С. 3-31.

We consider a monopolistic competition model with endogenous choice of technology in the closed economy case. The aim is to make comparative statistics of equilibrium and social optimal solutions with respect to "technological innovation"; parameter which influences on costs. Key findings: with the growth of innovation and investment in the production increase; behavior of the equilibrium variables depends only on the elasticity of demand; behavior of the socially optimal variables depends only on the elasticity of utility; behavior of the equilibrium and socially optimal variables does not depend on the properties of the cost as a function of R&D.

Added: Oct 18, 2014
Article
Яновская Е. Б. Математическая теория игр и ее приложения. 2014. Т. 6. № 1. С. 100-121.

A game with  {\em{restricted cooperation}} is a triple (N,v,\Omega), where N is a finite set of players, \Omega is  a non-empty collection oft feasible coalitions , and v a  characteristic function defined on \Omega. U.Faigle (1989) obtained necessary and sufficient conditions for the non-emptiness of the core for games with restricted cooperation. Unlike the classical TU games the cores for games with restricted cooperation may be unbounded. Recently Grabisch and Sudh\"olter (2012) studied the core for games whose collections of feasible coalitions has  a hierarchical structure generated by a partial order relation of players.For this class of games they proposed a new concept -- the bounded core -- whose definition can be  extended to the general class of games with restricted cooperation as  the union of all bounded faces of the core. For this class of games  the bounded core can be empty even the core is not empty. An axiomatization of the bounded core for the whole  class of games  with restricted cooperation is given with the help of axioms efficiency, boundedness, bilateral consistency, a weakening of converse consistency, and ordinality. Another axiomatization of the core is given for the subclass of games with non-empty cores that are bounded. The characterizing axioms are non-emptiness, covariance, boundedness, consistency, the reconfirmation property, superadditivity, and continuity.  

Added: Dec 24, 2014
Article
Кузютин Д. В., Никитина М. В., Панкратова Я. Б. Математическая теория игр и ее приложения. 2014. Т. 6. № 1. С. 19-40.
Added: Nov 9, 2014
Article
Петросян О. Л., Громова Е. В., Погожев С. В. Математическая теория игр и ее приложения. 2016. Т. 8. № 4. С. 79-106.
Added: Nov 24, 2017
Article
Петросян О. Л. Математическая теория игр и ее приложения. 2017.
Added: Oct 22, 2018
Article
Яновская Е. Б. Математическая теория игр и ее приложения. 2011. Т. 3. № 4. С. 23-48.

A cooperative game with restricted cooperation is a triple (N,v,Omega), where N is a finite set of players, Omega is a collection of  feasible} coalitions, v:Omega -->R is a characteristic function. The definition implies that if Omega=2^N, then the game (N,v,Omega)=(N,v) is a classical cooperative game with transferable utilities (TU). The class of all games with restricted cooperation  with an arbitrary {\it universal} set of players is considered. The prenucleolus for the class is defined in the same way as for classical TU games. Necessary and sufficient conditions on a collection Omega providing existence and singlevaluedness of the prenucleoli for the class into consideration are found.  Axiomatic characterizations of the prenucleolus for games with two-type collections Omega generated by coalitional structures

Added: Mar 20, 2014
Article
Матвеенко В. Д., Королев А. В. Математическая теория игр и ее приложения. 2016. Т. 8. № 1. С. 106-137.
Added: Apr 29, 2016
Article
Матвеенко В. Д., Королев А. В. Математическая теория игр и ее приложения. 2011. Т. 3. № 2. С. 50-80.

A contract theory model is studied in which objective functions of a regulator and of two types of firms include ecological variables. It is shown that the choice of a way of functioning of the regulating mechanism (separating or pooling) depends both on political conditions (what kind of regulator defines the mechanism and the contracts) and on economic conditions: a difference between ''dirty'' and ''green'' firms in their efficiency and a degree of their prevalence in the economy. Under a small difference in values of parameter characterizing the types of firms it is shown that if, what seems to be typical for many developing and transition economies, the use of ''dirty'' technologies increases the rentability of the firms and the fraction of ''dirty'' firms in the economy is high then the pooling (non-market, in some sense) mechanism is chosen more often. Under conditions which seem to be typical for industrial countries, where ''green'' firms are relatively efficient, a separating (more market) mechanism can be expected more often.

Added: Nov 17, 2012
Article
Яновская Е. Б. Математическая теория игр и ее приложения. 2017. Т. 9. № 3. С. 93-127.

Two-person games and cost/surplus sharing problems are worth for studying because they are the base for their extending to the classes of such problems with variable population with the help of very powerful consistency properties. In the paper a family of cost-sharing methods for cost sharing problems with two agents is extended to a class of solutions for two-person cooperative games that are larger than both cost-sharing and surplus-sharing problems, since cooperative games have no restrictions on positivity of costs and surpluses. The tool of the extension is a new invariance axiom - self covariance - that can be applied both to cost-sharing methods and to cooperative game solutions. In particular, this axiom replaces the Lower composition axiom which is not applicable to methods for profit sharing problems.

Added: Nov 27, 2017
Article
Крючков М. В., Русаков С. В. Математическая теория игр и ее приложения. 2015. Т. 7. № 2. С. 33-48.

This paper considers the case of making decisions under risk. The player is well-informed about all the possible states of nature, as well as the corresponding probabilities (or their statistical estimates) which help the nature implement the states. There is a finite number of games for the payoff matrix made. Moreover, its elements may vary depending on the outcome of each game. The paper offers some financial betting systems (strategies) such as a fixed bet, Kelly criterion, martingale method and some of its modifications. On small game intervals (3-5 games) there are calculations of performance indicators for these strategies. They are the calculations of performance indicators by Bayesian and the ones when the variance of winning is taken into consideration. In the final part of the paper the results of numerical experiments with elements of statistical modeling are given which allow us to give recommendations on the application of these strategies.

Added: Oct 1, 2015
Article
Крепс В. Л., Гаврилович М. Р. Математическая теория игр и ее приложения. 2019. Т. 11. № 1. С. 21-38.

Matrix games with incomplete information on both sides and public signal on the state of game represented by random binary code of fixed length are considered. Players are computationally bounded and are only able to play strategies to finite automata of different sizes: m for Player 1 and n for Player 2 where m ≫ n. We obtain a lower bound for m and an upper bound for n which may turn the original game with incomplete information for both players into a game with incomplete information for Player 2.

Added: May 31, 2019
Article
Сандомирская М. С., Доманский В. К. Математическая теория игр и ее приложения. 2012. Т. 4. № 1. С. 32-54.

We investigate a model of one-stage bidding between two differently informed stockmarket agents where one unit of risky asset (share) is traded. The random liquidation price of a share may take two values: the integer positive m with probability p and 0 with probability 1-p. Player 1 (insider) is informed about the price, Player 2 is not. Both players know probability p. Player 2 knows that Player 1 is an insider. Both players propose simultaneously their bids. The player who posts the larger price buys one share from his opponent for this price. Any integer bids are admissible. The model is reduced to zero-sum game with lack of information on one side. We construct the solution of this game for any p and m : we find optimal strategies of both players and describe recurrent mechanism for calculating game value. The results are illustrated by means of computer simulation.

Added: Apr 15, 2014
Article
Кацев И. В., Яновская Е. Б. Математическая теория игр и ее приложения. 2009. Т. 1. № 1. С. 46-66.

A collection of TU games solutions intermediate between the prekernel and the prenucleolus is considered. All these solutions are Davis-Maschler consistent, symmetric and covariant. Each solution from the collection is parametrized by a positive integer k such that for all games with the number of players not greater than k, the solution for parameter k coincides with the prenucleolus, and for games with more than k players it is maximal, i.e. it satisfies the "k-converse consistency". The properties of solutions are described and their characterization in terms of balancedness is given.  

Added: Mar 20, 2014
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