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## Cooperative Optimality Concepts for Games with Preference Relations

P. 421-432.

Savina T.

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 (acceptable outcomes) of games which are in a homomorphic relation. The main results of our work are connected with finding of covariant and contravariant homomorphisms.

### In book

Issue 4. , St. Petersburg : Graduate School of Management, St. Petersburg University, 2011

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 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

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

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., 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

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

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., 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

Savina T., , in : Game Theory and Management. Collected abstracts of papers presented on the Fourth International Conference Game Theory and Management. : St. Petersburg : Graduate School of Management, St. Petersburg University, 2010. P. 197-199.

В работе рассмотрен кооперативный аспект игры, введены понятия коалиционного гомоморфизма. ...

Added: March 19, 2013

Radionov S., Pospelov I. G., Mathematical Models and Computer Simulations 2014 Vol. 6 No. 5 P. 445-455

Based on the well-known model of monopolistic competition by Melitz with a finite number of firms, we built a number of dynamic models, designed to clarify the dynamic behavior of the original construction. Two variants of the formal Melitz dynamic model are presented, with the quasi-steady state found in one of them. Also, the models ...

Added: September 22, 2014

Golubin A. Y., ASTIN Bulletin 2008 Vol. 38 No. 2 P. 441-460

The concept of economic equilibrium under uncertainty is applied to a model of insurance market where, in distinction to the classic Borch's model of a reinsurance market, risk exchanges are allowed between the insurer and each insured only, not among insureds themselves. Conditions characterizing an equilibrium are found. A variant of the conditions, based on ...

Added: May 14, 2013

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

Alexander S. Belenky, Bolkunov D. S., Energy Systems 2016 Vol. 7 No. 4 P. 663-698

Added: March 1, 2016

Gurvich V., Naumova M., / Cornell University. Series "Working papers by Cornell University". 2024.

In several recent papers some concepts of convex analysis were extended to discrete sets. This paper is one more step in this direction. It is well known that a local minimum of a convex function is always its global minimum. We study some discrete objects that share this property and provide several examples of convex ...

Added: August 19, 2024

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

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

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

., 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

Kuzyutin D., Nikitina M., Марченко И. В., , in : European Meeting on Game Theory (SING11-GTM2015). Collected abstracts of papers presented on the European Meeting on Game Theory. : St. Petersburg : Graduate School of Management, St. Petersburg University, 2015. P. 117-118.

We investigate the vertical differentiation model in the insurance market taking into account fixed costs (the costs of quality improvement) of different structure. The subgame perfect equilibrium in a two-stage game is constructed for the case of compulsory insurance when firms use Bertrand-Nash or Stakelberg equilibria at the stage of price competition. For the ...

Added: October 20, 2015

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

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

Kuzyutin D., Nikitina M., Razgulyaeva L. et al., , 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. 176-186.

We investigate the vertical differentiation model in the insurance market taking into account fixed costs (the costs of quality improvement) of different structure. The subgame perfect equilibrium in a two-stage game is constructed for the case of compulsory insurance when firms use Bertrand-Nash or Stakelberg equilibria at the stage of price competition. For the case ...

Added: October 20, 2015

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