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Construction of a Strong Nash Equilibrium in a Class of Infinite Nonzero-Sum Games
Proceedings of the Steklov Institute of Mathematics. 2019. Vol. 305. P. 140–149.
Pankratova Y., Petrosyan L.
In our previous papers (2002, 2017), we derived conditions for the existence of a strong Nash equilibrium in multistage nonzero-sum games under additional constraints on the possible deviations of coalitions from their agreed-upon strategies. These constraints allowed only one-time simultaneous deviations of all the players in a coalition. However, it is clear that in real-world problems the deviations of different members of a coalition may occur at different times (at different stages of the game), which makes the punishment strategy approach proposed by the authors earlier inapplicable in the general case. The fundamental difficulty is that in the general case the players who must punish the deviating coalition know neither the members of this coalition nor the times when each player performs the deviation. In this paper, we propose a new punishment strategy, which does not require the full information about the deviating coalition but uses only the fact of deviation of at least one player of the coalition. Of course, this punishment strategy can be realized only under some additional constraints on stage games. Under these additional constraints, it was proved that the punishment of the deviating coalition can be effectively realized. As a result, the existence of a strong Nash equilibrium in the game was established.
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 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
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which
includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes
the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
Aleksandra L. Grinikh, , in: Contributions to Game Theory and Management, Vol. XVVol. 15.: St. Petersburg: Saint Petersburg State University, 2022. Ch. 7 P. 60–80.
This paper summarizes the list of our works that contain researches about optimality principles for the "n-person prisoner’s dilemma" game. The classic model is considered through the new payoff function for each player that allows to consider it without restrictions for the number of players. The new characteristic function gives an opportunity to introduce the ...
Added: October 31, 2024
Kuzyutin D., Smirnova N., Тантлевский И. Р., Математическая теория игр и ее приложения 2024 Т. 16 № 1 С. 61–77
The paper examines an infinite-horizon multistage game of renewable resource extraction with two types of players, differing in the discount rates of future payoffs. Using the dynamic programming method, a non-cooperative solution - a subgame perfect Nash equilibrium in stationary positional strategies, as well as a cooperative (Paretooptimal) solution for the case of complete cooperation ...
Added: April 12, 2024
Kuzyutin D., Skorodumova Y., Smirnova N., , in: Mathematical Optimization Theory and Operations Research, 21st International Conference, MOTOR 2022, Petrozavodsk, Russia, July 2–6, 2022, ProceedingsVol. 13367.: Springer, 2022. Ch. 17 P. 235–249.
Added: July 7, 2022
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
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
Smirnov S. N., Aequationes Mathematicae 2019 Vol. 93 No. 2 P. 445–449
In this short note we show that a weak version of Bernstein’s characterization of the normal distribution implies the local integrability of a measurable solution of the Cauchy functional equation; the linearity of a solution of the Cauchy functional equation is an easy consequence of its local integrability. In its turn, this weak version of ...
Added: December 26, 2019