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Equilibrium Points in Antagonistic Games with Preference Relations
P. 71-74.
Savina T.
In this paper the basic properties of different types of equilibrium concepts in antagonistic games with various preference structures are considered.
In book
Issue 2. , Saratov : Издательство Саратовского университета, 2011
Savina T., , in : Contributions to game theory and management. Issue 4.: St. Petersburg : Graduate School of Management, St. Petersburg University, 2011. P. 421-432.
In this paper we consider games with preference relations. The cooperative aspect of a game is connected with its coalitions. The main optimality concepts for such games are concepts of equilibrium and acceptance. We introduce a notion of coalition homomorphism for cooperative games with preference relations and study a problem concerning connections between equilibrium points ...
Added: February 18, 2013
Savina T., , in : Contributions to game theory and management. Issue 3.: St. Petersburg : Graduate School of Management, St. Petersburg University, 2010. P. 387-398.
In this paper we consider games with preference relations. The main optimality concept for such games is concept of equilibrium. We introduce a notion of homomorphism for games with preference relations and study a problem concerning connections between equilibrium points of games which are in a homomorphic relation. The main result is finding covariantly and ...
Added: March 19, 2013
Savina T., Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика 2011 Т. 11 № 2 С. 32-36
For n person games with preference relations some types of optimality solutions are introduced. Elementary properties of their solutions are considered. One sufficient condition for nonempty Ca-core is found. ...
Added: January 20, 2013
Bykadorov I., / Economics Education and Research Consortium. Series "EERC Working Paper Series". 2010. No. 10/03E.
In Russia the chain-stores gained a considerable market power. In the paper we combine a Dixit-Stiglitz industry with a
monopolistic retailer. The questions addressed are: Does the retailer always deteriorate welfare, prices and variety of goods?
Which market structure is worse: Nash or Stackelberg behavior? What should be the public policy in this area? ...
Added: November 17, 2013
Savina T., Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика 2009 Т. 9 № 3 С. 66-70
Для игр с отношениями предпочтения мы рассматриваем в качестве принципов оптимальности равновесие по Нэшу, а также некоторые его модификации. Для описания оптимальных решений игр с отношениями предпочтения введены ковариантно и контравариантно полные семейства гомоморфизмов. ...
Added: January 20, 2013
Аевский В. В., Андрюшкевич О. А., Беленький В. З. et al., М. : ЦЭМИ РАН, 2012
The ninth issue of annual Collection of articles consists of four sections: “Analysis of actual economic processes”, “Modeling of financial and market mechanisms”, “Dynamic models”, “Discussions, Notes and Letters”. As a whole nine articles are presented ...
Added: February 13, 2014
Savina T., В кн. : Математика. Механика: сборник научных трудов. Вып. 13.: Саратов : Издательство Саратовского университета, 2011. С. 92-95.
В отличие от классической теории игр целевая структура игры с отношениями предпочтения задается не функциями выигрыша, а рефлексивными бинарными отношениями. Оптимальными решениями в данном классе игр являются равновесие, равновесие по Нэшу и допустимые (вполне допустимые) исходы. Результатом данной работы является ряд теорем о точном описании множества оптимальных решений (а именно, ситуаций равновесия и ситуаций равновесия ...
Added: February 18, 2013
Pankratova Y., Petrosyan L., В кн. : Lecture Notes in Computer Science. Vol. 11548.: Springer, 2019. С. 685-696.
In the paper, a two-level infinitely repeated hierarchical game with one player (center) C0 on the first level and S1...Sn subordinate players on the second is considered. On each stage of the game player C0 selects vector x=(x1....xn) from a given set X, in which each component represents a vector of resources delivered by C0 to one of the ...
Added: October 26, 2019
Matveenko V. D., Korolev A. V., , in : Proceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics. Issue 22.: University of Turku, 2017. P. 119-135.
We study game equilibria in a network, in each node of which an economy is described by a two-period model of endogenous growth with production and knowledge externalities. Each node obtains an externality produced by the sum of knowledge in neighbour nodes. Uniqueness of the inner equilibrium is proved. Ways of behaviour of agent (passive, ...
Added: June 8, 2017
Matveenko V. D., Korolev A. V., Бахтин М. А., В кн. : Математика, статистика и информационные технологии в экономике, управлении и образовании. Ч. 1: Математика и статистика.: Тверь : Тверской государственный университет, 2016. С. 79-84.
This paper studies a model of game interaction on a network with externalities, in which agents choose their levels of investment. We compare two concepts of equilibrium: standard Nash definition and “Jacobian” definition of equilibrium with externalities. It is shown that the equilibrium level of investment is equal to the agent’s alpha centrality. Also, we ...
Added: February 23, 2017
Korolev A. V., Ougolnitsky G. A., International Game Theory Review 2023 Vol. 25 No. 2 Article 2350004
In this paper, we build and investigate cooperative games with different characteristic
functions (von Neumann–Morgenstern, Petrosyan–Zaccour, Gromova–Petrosyan) on the
base of symmetrical Cournot oligopoly game-theoretic models in normal form. We find
Nash and Stackelberg equilibria and cooperative solutions for nonsymmetrical Cournot
oligopoly game-theoretic models in normal form. Also, we build and investigate coop27
erative three-player games with the same characteristic ...
Added: January 26, 2023
Switzerland : Springer Publishing Company, 2020
In this paper, we consider the following problem - what affects the Nash equilibrium amount of investment in knowledge when one of the complete graph enters another full one. The solution of this problem will allow us to understand exactly how game agents will behave when deciding whether to enter the other net, what conditions ...
Added: June 23, 2019
Gurvich V., Boros E., Milanič M. et al., Discrete Applied Mathematics 2018 Vol. 243 P. 21-38
We give an example of a three-person deterministic graphical game that has no Nash equilibrium in pure stationary strategies. The game has seven positions, four outcomes (a unique cycle and three terminal positions), and its normal form is of size 2×2×4 only. Thus, the example strengthens significantly the one obtained in 2014 by Gurvich and Oudalov; the ...
Added: October 10, 2018
Samoylenko I., Кулешов И. В., Райгородский А. М., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 355-368
At the middle of the 2000-th, scientists studying the functioning of insect communities identified four basic patterns of the organizational structure of such communities. (i) Cooperation is more developed in groups with strong kinship. (ii) Cooperation in species with large colony sizes is often more developed than in species with small colony sizes. And small-sized ...
Added: July 28, 2023
Gurvich V., Koshevoy G., Discrete Applied Mathematics 2018 P. 1-15
Given two finite ordered sets A and B, let O=A×B denote the set of outcomes of the following game: Two players, Alice and Bob, have the sets of strategies X and Y that consist of all monotone non-decreasing mappings x:A→B and y:B→A, respectively. It is easily seen that each pair (x,y)∈X×Y produces at least one deal, that is, an outcome (a,b)∈O such that x(a)=b and y(b)=a. Denote by G(x,y)⊆O the set of all such deals related to (x,y). ...
Added: October 10, 2018
Matveenko V. D., Korolev A. V., , in : Contributions to game theory and management / Ed. by L. A. Petrosyan, N. A. Zenkevich. Issue 8. St. Petersburg : Graduate School of Management, St. Petersburg University, 2015. Issue 8.: St. Petersburg : Graduate School of Management, St. Petersburg University, 2015. P. 199-222.
We consider a game equilibrium in a network in each node of which an economy is described by the simple two-period model of endogenous growth with production and knowledge externalities. Each node of the network obtains an externality produced by the sum of knowledge in neighbor nodes. Uniqueness of the inner equilibrium is proved. Three ...
Added: September 22, 2015
Belenky A., Egorova L. G., , in : Optimization and Its Applications in Control and Data Sciences: In Honor of Boris T. Polyak’s 80th Birthday (Springer Optimization and Its Applications). Book 115.: Springer, 2016. P. 51-117.
The paper proposes two new approaches to designing efficient mathematical tools for quantitatively analyzing decision-making processes that small and medium price-taking traders undergo in forming and managing their portfolios of financial instruments traded in a stock exchange. Two mathematical models underlying these approaches are considered. If the trader can treat price changes for each financial ...
Added: October 10, 2016
Pankratova Y., Petrosyan L., , in : Stability and Control Processes: Proceedings of the 4th International Conference Dedicated to the Memory of Professor Vladimir Zubov. : Cham : Springer, 2022. Ch. 65. P. 447-455.
Added: June 5, 2022
Levando D. V., / SSRN. Series "Working Papers". 2017.
Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This paper suggests an approach to this problem in the framework of a noncooperative game theory. Definition of a suggested finite game includes a family of nested simultaneous non-cooperative finite games with intra- and inter-coalition externalities. In this family, ...
Added: May 3, 2017
Averboukh Y., Труды института математики и механики УрО РАН 2014 Т. 20 № 3 С. 26-40
В работе рассматриваются дифференциальные игры конечного числа лиц в классе стратегий с поводырем, предложенных Н. Н. Красовским и А. И. Субботиным. Строится набор стратегий, обеспечивающий равновесие по Нэшу в любой начальной позиции из заданного компакта. Конструкция решения основана на многозначной функции, удовлетворяющей некоторым условиям стабильности. Доказано существование функции цены. ...
Added: April 22, 2020
., 2019
In this paper, we consider the following problem - what affects
the Nash equilibrium amount of investment in knowledge when some agents
of the complete graph enter another full one. The solution of this problem will
allow us to understand exactly how game agents will behave when deciding
whether to enter the other net, what conditions and externalities affect it
and ...
Added: September 29, 2019
Levando D. V., / Cornell University. Series arXiv "math". 2016. No. arXiv:1612.02344.
The paper defines a non-cooperative simultaneous finite game to study coalition structure formation with intra and inter-coalition externalities. The novelty of the game is that the game definition embeds a \textit{coalition structure formation mechanism}. This mechanism portions a set of strategies of the game into partition-specific strategy domains, what makes every partition to be a ...
Added: December 8, 2016
Филатов А. Ю., / Preprints.org. Series 02:43:16 "CEST". 2023.
The paper proposes a game theory model of price oligopoly with a heterogeneous product, where total demand depends linearly on the minimum market price. This model develops the Bertrand oligopoly for the case of imperfect price elasticity of demand. The most interesting result is an asymmetric Nash equilibrium with different prices and sales in the ...
Added: January 10, 2024
Networks Structure, Equilibria, and Adjustment Dynamics in Network Games with Nonhomogeneous Players
Гармаш М. В., Уткина А. А., Korolev A. V., , in : Contributions to Game Theory and Management Volume XII. Vol. XII.: ., 2019. P. 128-139.
In this paper, we consider the following problem - what affects
the Nash equilibrium amount of investment in knowledge when some agents
of the complete graph enter another full one. The solution of this problem will
allow us to understand exactly how game agents will behave when deciding
whether to enter the other net, what conditions and externalities affect it
and ...
Added: September 29, 2019