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## On Nash Equilibrium in Repeated Hierarchical Games

Ch. 65. P. 447-455.

Pankratova Y., Petrosyan L.

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

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., , 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

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

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

Sandomirskaia M., В кн. : Экономический рост, ресурсозависимость и социально-экономическое неравенство: материалы IV Всероссийской конференции 27-29 октября 2014 года. : СПб. : Издательство Нестор-История, 2014. С. 218-220.

We consider a model of location-price competition between two firms, located on the circle. Nash equilibrium, equilibrium in secure strategies, and Nash-2 equilibrium are compared. We demonstrate that Nash-2 equilibrium exists for any locations of firms. The set of Nash-2 equilibria is treated as tacit collusion. ...

Added: October 15, 2015

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 : 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

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

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

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

Bykadorov I., Product Diversity in a Vertical Distribution Channel under Monopolistic Competition / 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

Averboukh Y., Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 2017 Vol. 27 No. 3 P. 299-308

The paper is concerned with the randomized Nash equilibrium for a nonzero-sum deterministic differential game of two players. We assume that each player is informed about the control of the partner realized up to the current moment. Therefore, the game is formalized in the class of randomized non-anticipative strategies. The main result of the paper ...

Added: April 17, 2020

Pankratova Y., Петросян Л. А., Lecture Notes in Computer Science 2019 Vol. 11548 P. 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 5, 2019

Levando D. V., Formation of coalition structures as a non-cooperative game 1: theory / 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

., 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., Formation of Coalition Structures as a Non-Cooperative Game / 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

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

Savina T., , in : Представляем научные достижения миру. Естественные науки: материалы научной конференции молодых ученых "Presenting Academic Achievements to the World". Issue 2.: Saratov : Издательство Саратовского университета, 2011. P. 71-74.

In this paper the basic properties of different types of equilibrium concepts in antagonistic games with various preference structures are considered. ...

Added: February 18, 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

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

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

Korolev A. V., Ougolnitsky G. A., International Game Theory Review 2022 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

Matveenko V. D., Korolev A. V., Бахтин М. А., В кн. : Государство и бизнес. Современные проблемы экономики. Материалы VIII международной научно-практической конференции. Том 1. Т. 1.: СПб. : РАНХиГС, 2016. С. 77-83.

This paper studies a model of game interaction with externalities on a network, in which agents choose their level of investment. We compare two concepts of equilibrium: standard Nash definition and “Jacobian” definition of equilibrium with externalities. It is shown that in both cases agents may be passive, active and hyperactive, and conditions for optimality ...

Added: February 24, 2017