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Approximate Solutions of Continuous-Time Stochastic Games
SIAM Journal on Control and Optimization. 2016. Vol. 54. No. 5. P. 2629-2649.
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a model game. The dynamics of the model game differs from the original one. The general result applied to differential games yields the approximation of value function of differential game by the solution of countable system of ODEs.
Petrosian O., Погожев С. В., Automatica 2018
Added: February 18, 2018
Landim C., Mariani M., Seo I., Archive for Rational Mechanics and Analysis 2019 Vol. 231 No. 2 P. 887-938
We present two variational formulae for capacity in the context of non-selfadjoint elliptic operators. The minimizers of these variational problems are expressed as solutions of boundary-value elliptic equations. We use these principles to provide a sharp estimate for the transition times between two different wells for non-reversible diffusion processes. This estimate permits us to describe ...
Added: October 3, 2018
Afanasiev V., IFAC-PapersOnLine 2016 Vol. 49 No. 12 P. 360-365
The problem of optimal control for a class of non-linear objects with uncontrolled bounded disturbances is formulated in the sense of a differential game. In case of problems with quadratic quality functional, the problem of optimal control search is reduced to finding of solution of Hamilton-Jacobi-Isaacs equation. Solutions of this equation at the rate of ...
Added: December 23, 2016
Silvanovich O. V., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2018 Vol. 51 No. 3 P. 267-275
For more than a century, the constructive description of functional classes in terms of the possible rate of approximation of its functions by means of functions chosen from a certain set remains among the most important problems of approximation theory. It turns out that the nonuniformity of the approximation rate due between the points of ...
Added: November 26, 2018
Yashunsky A., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2020 Vol. 14 No. 3 P. 581-591
We consider the transformations of independent random variables over a linearly ordered finite set (a chain) by the join and meet operations. We investigate the possibility of approximating an arbitrary probability distribution on a chain by means of a (possibly iterated) application of the join and meet operations to independent random variables with distributions from ...
Added: July 6, 2021
Shvedov A. S., Mathematical notes 2020 Vol. 107 No. 4 P. 679-686
Noncooperative discounted stochastic n-person games are considered; the payoffs at each step are represented by trapezoidal fuzzy numbers. The existence of stationary Nash equilibrium strategies is proved. ...
Added: April 9, 2020
Zaremba A., Gromova E., Tur A., Mathematics 2020 Vol. 8 No. 12 Article 2185
One class of differential games with random duration is considered. It is assumed that the duration of the game is a random variable with values from a given finite interval. The cumulative distribution function (CDF) of this random variable is assumed to be discontinuous with two jumps on the interval. It follows that the player’s ...
Added: January 31, 2021
Molchanov S., Bogachev L., Derfel G., Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 2015 Vol. 471 P. 1-19
Added: June 22, 2016
Shvedov A. S., Математические заметки 2020 Т. 107 № 4 С. 623-632
Рассматриваются некооперативные дисконтированные стохастические игры с n участниками, при этом выигрыши на каждом шаге представляются трапецоидальными нечеткими числами. Доказывается существование стационарных равновесных по Нэшу стратегий. ...
Added: April 9, 2020
Averboukh Y., Mathematics 2018 Vol. 6 No. 9 P. 151
The paper is devoted to inverse Stackelberg games with many players. We consider both static and differential games. The main assumption of the paper is the compactness of the strategy sets. We obtain the characterization of inverse Stackelberg solutions and under additional concavity conditions, establish the existence theorem. ...
Added: April 17, 2020
Averboukh Y., IFAC-PapersOnLine 2018 Vol. 51 No. 32 P. 654-658
The paper is concerned with the mean field type differential game that describes the behavior of the large number of similar agents governed by the unique decision maker and influenced by disturbances. It is assumed that the decision maker wishes to bring the distribution of agents onto the target set in the space of probabilities ...
Added: April 17, 2020
Averboukh Y., Proceedings of the VIII International Conference on Optimization and Applications (OPTIMA-2017) 2017 Vol. 1987 P. 73-80
The paper is concerned with approximations of a value function of a differential game. To this end we introduce a approximation of the original differential game by a continuous-time Markov game with infinite state space. The value function of this game in a given region is approximated by a solution of a finite state Markov ...
Added: April 17, 2020
Tumanov M., Piunovskly A., Plakhov A., Optimal Control Applications and Methods 2019 P. 1-21
Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the optimality equation. The theory is illustrated by an example from mathematical epidemiology. The developed methods can be also useful for ...
Added: February 27, 2020
Averboukh Y., AIP Conference Proceedings 2017 Vol. 1907 P. 030048-1-030048-5
The note is concerned with the theory of many players differential games examined within the framework of mean field approach. The results presented in the note are as follows. First, we show that the solution to the deterministic mean field game can be nonunique. Second, we present a property of the multifunction of the mean ...
Added: April 17, 2020
Veretennikov A., Veretennikova M., / Cornell University. Series "Working papers by Cornell University". 2019.
New convergence rate asymptotic bound for a class of homogeneous Markov chains is established. ...
Added: November 14, 2019
Olshanski G., / Cornell University. Series math "arxiv.org". 2013. No. 1310.6155.
These are notes for a mini-course of 3 lectures given at the St. Petersburg
School in Probability and Statistical Physics (June 2012). My aim was to
explain, on the example of a particular model, how ideas from the
representation theory of big groups can be applied in probabilistic problems.
The material is based on the joint paper arXiv:1009.2029 by ...
Added: November 16, 2013
Gromova E., Malakhova A., Palestini A., Mathematics 2018 Vol. 6 No. 9 P. 1-17
A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the cumulative distribution function (c.d.f.) of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of ...
Added: March 11, 2020
Borodin A., Olshanski G., Journal of Functional Analysis 2012 Vol. 263 P. 248-303
We construct a four-parameter family of Markov processes on infinite Gelfand–Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary of the Gelfand–Tsetlin graph or, equivalently, the space of extreme characters of the infinite-dimensional unitary group U(∞). The process has a ...
Added: February 25, 2013
Yashunsky A., Algebra Universalis 2019 Vol. 80 No. 1 (5) P. 1-16
We consider the problem of approximating distributions of Bernoulli random variables by applying Boolean functions to independent random variables with distributions from a given set. For a set B of Boolean functions, the set of approximable distributions forms an algebra, named the approximation algebra of Bernoulli distributions induced by B. We provide a complete description ...
Added: September 9, 2020
Semin V. G., Качество Инновации Образование, РФ.Москва.Европейский центр по качеству 2014 № 11 С. 61-66
The article presents the results of stochastic modeling of flow of power in a hierarchical structure of the political model of Government - civil society using the apparatus of the equations of Fokker-Planck-Kolmogorov equation. These results are a further development of the well-known mathematical implementation of the General scheme of the system "power-society"that describes the ...
Added: March 14, 2015
Puzino Y. A., Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния 2014 № 22 С. 46-52
The increasing of the efficiency of technological modes of steel products manufacturing requires simulation of metal forming during hot deformation. To obtain correct results, one should set the correct initial and boundary conditions, including the mechanical properties of materials, which represent the dependence of the stress-strain and strain rate at maintained temperature.
In the experiments one ...
Added: January 19, 2015
Yashunsky A., Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 1 P. 217-221
We consider transformations of random variables on finite sets by algebraic operations. A system of operations is said to be approximation complete if any random variable may be approximated with arbitrary precision by applying the given operations to mutually independent identically distributed random variables whose distributions have no zero components. We establish some necessary conditions ...
Added: July 6, 2021
Averboukh Y., Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 2017 Vol. 27 No. 3 P. 299-308
The paper is concerned with the randomized Nash equilibrium for a nonzero-sum deterministic differential game of two players. We assume that each player is informed about the control of the partner realized up to the current moment. Therefore, the game is formalized in the class of randomized non-anticipative strategies. The main result of the paper ...
Added: April 17, 2020
García-Meza M. A., Gromova E., López-Barrientos J. D., International Game Theory Review 2018 Vol. 20 No. 3
In this paper, we develop a dynamic model of an oligopoly playing an advertising game of goodwill accumulation with random terminal time. The goal is to find a cooperative solution that is time-consistent, considering a dynamic accumulation of goodwill with depreciation for a finite number of firms. ...
Added: March 13, 2020