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## Time consistent cooperative solutions for multistage games with vector payoffs

Operations Research Letters. 2017. Vol. 45. No. 3. P. 269-274.

Kuzyutin D., Bartel M.

To ensure sustainable cooperation in multistage games with vector payoffs we use the payment schedule based approach. The main dynamic properties of cooperative solutions used in single-criterion multistage games are extended to multicriteria games.

We design two recurrent payment schedules that satisfy such advantageous properties as the efficiency and the time consistency conditions, non-negativity and irrational behavior proofness.

Kuzyutin D., Lipko I., Pankratova Y. et al., , in: Frontiers of Dynamic Games Game Theory and Management, St. Petersburg, 2019. .: Birkhauser/Springer, 2020.. Ch. 10. P. 141-159.

To enforce the long-term cooperation in a multistage multicriteria game we use the imputation distribution procedure (IDP) based approach. We mainly focus on such useful properties of the IDP like “reward immediately after the move” assumption, time consistency inequality, efficiency and non-negativity constraint. To overcome the problem of negative payments along the optimal cooperative trajectory ...

Added: January 29, 2021

Kuzyutin D., Громова Е. В., Pankratova Y., Operations Research Letters 2018 Vol. 46 No. 6 P. 557-562

We use the imputation distribution procedure approach to ensure sustainable cooperation in a multistage game with vector payoffs. In order to choose a particular Pareto optimal and time consistent strategy profile and the corresponding cooperative trajectory we suggest a refined leximin algorithm. Using this algorithm we design a characteristic function for a multistage multicriteria game. Furthermore, we provide sufficient conditions for strong time consistency of the core. ...

Added: November 6, 2018

Kuzyutin D., Pankratova Y., Светлов Р., , in: Frontiers of Dynamic Games, Game Theory and Management, St. Petersburg, 2018. .: Birkhäuser, 2019.. P. 85-102.

We deal with multistage multicriteria games in extensive form and employ so-called “A-subgame” concept to examine dynamical properties of some non-cooperative and cooperative solutions. It is proved that if we take into account only the active players at each A-subgame the set of all strong Pareto equilibria is time consistent but does not satisfy dynamical ...

Added: October 5, 2019

Grinikh A., , in: Contributions to Game Theory and Management Volume XII. Vol. XII.: ., 2019.. P. 151-158.

A cooperative finite-stage dynamic n-person prisoner's dilemma is considered. The time-consistent subset of the core is proposed. The Shapley value for the stochastic model of the n-person prisoner's dilemma is calculated in explicit form. ...

Added: October 31, 2019

Kuzyutin D., Smirnova N., Mathematics 2020 Vol. 8 No. 7 P. 1061

We design a mechanism of the players’ sustainable cooperation in multistage n-person game in the extensive form with chance moves. When the players agreed to cooperate in a dynamic game they have to ensure time consistency of the long-term cooperative agreement. We provide the players’ rank based (PRB) algorithm for choosing a unique cooperative strategy ...

Added: October 30, 2020

Kuzyutin D., Bartel M., Contributions to Game Theory and Management 2014 No. 7 P. 181-191

Using some specific approach to the coalition-consistency analysis in n-person multicriteria games we introduce two re¯nements of (weak Pareto) equilibria: the strong and strictly strong (n-1)-equilibriums. Axiomatization of the strictly strong (n-1)-equilibria (on closed families of multicriteria games) is provided in terms of consistency, strong one-person rationality, suitable variants of Pareto optimality and converse consistency ...

Added: November 9, 2014

Kuzyutin D., Gromova E., Smirnova N., , in: Mathematical Optimization Theory and Operations Research, 19th International Conference, MOTOR 2020, Novosibirsk, Russia, July 6–10, 2020, (Т. 12095). .: Cham: Springer, 2020.. P. 184-199.

We consider a class of multistage multicriteria games in extensive form with chance moves where the players cooperate to maximize their expected joint vector payoff. Assuming that the players have agreed to accept the minimal sum of relative deviations rule in order to choose a unique Pareto optimal payoffs vector, we prove the time consistency ...

Added: October 31, 2020

Grinikh A., Petrosyan L., , in: Journal of Physics: Conference Series 1864 (2021) 012061. Vol. 1864: 13th Multiconference on Control Problems (MCCP 2020) . Issue 1.: State Research Center of the Russian Federation CONCERN CSRI ELEKTROPRIBOR, JSC., 2021..

n-Person prisoner’s dilemma is a Markovian sequence of static games that are realized randomly depending on players' previous choices. The dynamic Shapley value is constructed in this case. The work is a continuation of the paper published earlier by Grinikh A. L. [1]. In this paper, we consider the new approach of dynamics of game ...

Added: September 29, 2021

Petrosyan L., Yeung D., Pankratova Y., , in: Mathematical Optimization Theory and Operations Research: Recent Trends: 20th International Conference, MOTOR 2021, Irkutsk, Russia, July 5–10, 2021, Revised Selected Papers. .: Cham: Springer, 2021.. P. 403-416.

A class of cooperative differential games on networks is considered. It is supposed that players have the possibility to cut connections with neighbors at each time instant of the game. This gives the possibility to compute the values of a characteristic function for each coalition as a joint payoff of players from this coalition without ...

Added: November 1, 2021

Kuzyutin D., Bartel M., , in: 2017 Consrtuctive nonsmooth analysis and related topics (dedicated to the memory of V.F.Demyanov) (CNSA). .: IEEE, 2017.. P. 178-181.

We use the payment schedule based approach to ensure stable cooperation in multistage games with vector payoffs. ...

Added: December 25, 2017

Kuzyutin D., Bartel M., , in: Abstracts of the International Conference «Constructive Nonsmooth Analysis and Related Topics» Dedicated to the Memory of Professor V. F. Demyanov. * 2.: St. Petersburg: ВВМ, 2017.. P. 202-206.

We use so-called “Imputation Distribution Procedure” approach to sustain long-term cooperation in n-person multicriteria game in extensive form. ...

Added: June 17, 2017

Smirnova N., Тарашнина С. И., TOP 2017

We investigate a new solution concept of a TU-game --- the $\alpha$-prenucleoli set. For an arbitrary $3$-person TU-game we construct analytical formulas for calculating the considered solution. Since the $\alpha$-prenucleoli set always contains the pre\-nucleolus and the $SM$-nucleolus the analytical formulas for calculating these solution concepts have also been verified. ...

Added: October 17, 2016

Petrosian O., Погожев С. В., Automatica 2018

Added: February 18, 2018

Petrosian O., Барабанов А. Е., Journal of Optimization Theory and Applications 2017 Vol. 172 No. 1 P. 328-347

In this study, a novel approach for defining and computing a solution for a differential game is presented for a case, wherein players do not have complete information about the game structure for the full time interval. At any instant in time, players have certain information about the motion equations and payoff functions for a ...

Added: November 24, 2017

Gusev V., Automation and Remote Control 2017 Vol. 10 No. 78 P. 1883-1891

В работе исследуется простая модель кооперативной игры патрулирования с коалиционной структурой. Показано, что векторы Шепли, Оуэна и Ауманна-Дрезе в рассматриваемой игре совпадают друг с другом при нечетном количестве патрулирующих. ...

Added: October 14, 2020

Petrosyan L., Yeung D., Pankratova Y., Proceedings of the Steklov Institute of Mathematics 2021 Vol. 27 No. 3 P. 286-295

In the paper, the differential games on networks with partner sets are considered. The payoffs of a given player depend on his actions and the actions of the players from his partner set. The cooperative version of the game is proposed, and a special type of characteristic function is introduced. It is proved the constructed ...

Added: November 1, 2021

Kuzyutin D., Bartel M., Razgulyaeva L., Applied Mathematical Sciences 2015 Vol. 9 No. 92 P. 4565-4573

Using A-optimality concept for vector-valued maximization, we propose a refinement of Pareto equilibria in n-person multicriteria games. The theorems on existence of A-equilibria and subgame perfect Aequilibria are derived. Time consistency of A-equilibria in extensive multicriteria games with perfect and incomplete information is proved. ...

Added: October 9, 2015

Bershtein M., Feigin B. L., Merzon G., Selecta Mathematica, New Series 2018 Vol. 24 No. 1 P. 21-62

We study plane partitions satisfying condition a_{n+1,m+1}=0 (this condition is called “pit”) and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions. Such plane partitions label the basis vectors in certain representations of quantum toroidal gl1 algebra, therefore our formulas can be interpreted as the characters of ...

Added: October 24, 2018

Akbarov S. S., Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016

Ilyashenko Y., Яковенко С. Ю., М.: МЦНМО, 2013

Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...

Added: February 5, 2014

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Kalyagin V. A., Koldanov A. P., Koldanov P. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70

A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...

Added: July 19, 2014

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624

Added: February 27, 2013