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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.
Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 P. 1–16
A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...
Added: May 21, 2026
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Gonchenko S., Lerman L., Turaev D., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Khutorskaya O., Stepochkina A. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2026 Vol. 12 No. 1 P. 60–110
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., V. N. Sivkin, Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
Petrosyan L. A., Pankratova Y., Doklady Mathematics 2023 Vol. 108 No. 1 P. S92–S99
Network differential games with partner sets are considered. The payoff of each player depends on his actions and the actions of the players from his partner set. The article proposes a cooperative version of the game. A special-type characteristic function that takes into account players in partner sets is introduced, and its superadditivity is proved. ...
Added: March 20, 2024
Tamara Teplova, Tatiana Sokolova, David Kissa, Resources Policy 2023 Vol. 86 No. B Article 104253
The purpose of the paper is to reveal the impact of different environment, social, and corporate governance (ESG) indicators on stock liquidity in the emerging Russian market, which is heavily dominated by the natural resources sector. We first apply Explainable Artificial Intelligence (AI) to identify and rank determining factors for stock liquidity on a sample ...
Added: October 23, 2023
Ignatov D. I., Kwuida L., Annals of Mathematics and Artificial Intelligence 2022 Vol. 90 No. 11 P. 1197–1222
We propose the usage of two power indices from cooperative game theory and public choice theory for ranking attributes of closed sets, namely intents of formal concepts (or closed itemsets). The introduced indices are related to extensional concept stability and are also based on counting of generators, especially of those that contain a selected attribute. ...
Added: January 31, 2023
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
Grinikh A., Petrosyan L., , in: 13th Multiconference on Control Problems (MCCP 2020) 6-8 October 2020, Saint Petersburg, RussiaVol. 1864.: IOP Publishing, 2021. Ch. 012061.
Added: September 29, 2021
Kuzyutin D., Lipko I., Pankratova Yaroslavna 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., 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
Antipov E. A., Pokryshevskaya E. B., Journal of Revenue and Pricing Management 2020 No. 19 P. 355–364
Forecasting demand and understanding sales drivers are one of the most important tasks in retail analytics. However, traditionally, linear models and/or models with a small number of predictors have been predominantly used in sales modeling. Taking into account that real-world demand is naturally determined by complex substitution and complementation patterns among a large number of ...
Added: October 31, 2020
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
Ignatov D. I., Kwuida L., , in: Ontologies and Concepts in Mind and Machine. 25th International Conference on Conceptual Structures, ICCS 2020.: Springer, 2020. P. 90–102.
Among the family of rule-based classification models, there are classifiers based on conjunctions of binary attributes. For example, the JSM-method of automatic reasoning (named after John Stuart Mill) was formulated as a classification technique in terms of intents of formal concepts as classification hypotheses. These JSM-hypotheses already represent an interpretable model since the respective conjunctions ...
Added: October 30, 2020