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## Cooperative Differential Games with Partner Sets on Networks

Proceedings of the Steklov Institute of Mathematics. 2021. Vol. 27. No. 3. P. 286-295.

Petrosyan L., Yeung D., Pankratova Y.

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 cooperative game is convex. Using the properties of the payoff functions and the constructed characteristic function, the Shapley Value and $\tau$-value are computed. It is also proved that in this special class of differential games the Shapley value is time-consistent.

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

Karpov A. V., Mathematical Social Sciences 2015 Vol. 74 P. 1-7

This paper studies the incentives for alliance (coalition) formation. It provides an example of an alliance
that leads to unlimited seat gains. A full description of a set that guarantees the lack of successful alliance
is found. The probability of the lack of successful alliances is evaluated. A game-theoretical approach for
alliance formation is applied. ...

Added: January 11, 2015

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

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

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

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

Kuzyutin D., Bartel M., Operations Research Letters 2017 Vol. 45 No. 3 P. 269-274

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 ...

Added: October 24, 2016

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

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

Antipov E. A., Pokryshevskaya E. B., Economics Bulletin 2014 Vol. 34 No. 4 P. 2368-2376

In this study we demonstrate how publicly available data can be used to work out the indirect importance of various hotel attributes for their visitors. We apply Shapley value decomposition of the recommendation rate to compute the percentage contributions of various attributes to the overall loyalty, which helps us explain why some of Cyprus hotels ...

Added: March 24, 2015

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., 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., 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

Karpov A. V., Journal of Informetrics 2014 Vol. 8 No. 1 P. 71-76

The publication credit allocation problem is one of the fundamental problems in bibliometrics. There are two solutions which do not use any additional information: equal weights measure and the Shapley value. The paper justifies the equal weights measure by showing equivalence with the Shapley value approach for sharing co-authors performance in specific games. ...

Added: November 23, 2013

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

Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66

Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...

Added: August 27, 2016

Arzhantsev I., Journal of Lie Theory 2000 Vol. 10 No. 2 P. 345-357

Added: July 8, 2014

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala: University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

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

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...

Added: March 13, 2016

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

Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293

Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...

Added: September 29, 2014