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Infinite Horizon Dynamic Games: A New Approach via Information Updating
International Game Theory Review. 2017. Vol. 19. No. 4. P. 1–23.
Petrosian O., Yeung D.
We introduce a new sequential game, where each player has a limited resource that he needs to spend on increasing the probability of winning each stage, but also on maintaining the assets that he has won in the previous stages. Thus, the players’ strategies must take into account that winning at any given stage negatively affects the chances of winning in later stages. Whenever the initial resources of the players are not too small, we present explicit strategies for the players, and show that they are a Nash equilibrium, which is unique in an appropriate sense.
Keywords: dynamic gameslooking forward approachinfinite game horizoninformation updatinguncertain payoff structures
Publication based on the results of:
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A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
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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 ...
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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, ...
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Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
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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 ...
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Medvedev V., / Series arXiv "math". 2026.
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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 ...
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Vorchik A., / Social Science Research Network. Серия SSRN Working Paper Series "SSRN Working Paper Series". 2026.
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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.
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In this paper, we develop a formal mathematical model aimed to explain the Dunning-Kruger effect that beginners systematically overestimate their own competence in various fields of knowledge and activity. We argue that the Dunning-Kruger effect arises from the emotional nature of confidence combined with unknown unknowns that it simply can not take into account due ...
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Musaev A. U., Vorchik A., / Series Social Science Research Network "Social Science Research Network". 2026.
This paper attempts to model the evolutionary theory of modernization and democratization. The model reflects the key provisions of R. Inglehart and C. Welzel's theory and provides a microfoundation for the adaptation of subjective values to the objective importances of the survival factors and the structure of the labour markets from the perspective of evolutionary ...
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Smirnov A., Starkov E., European Economic Review 2025 Vol. 178 Article 105113
This paper studies strategic communication in the context of social learning. Product reviews are used by consumers to learn product quality, but in order to write a review, a consumer must be convinced to purchase the item first. When reviewers care about the welfare of future consumers, this leads to a conflict: a reviewer today ...
Added: November 3, 2025
Kolokoltsov V., малафеев о. а., Singapore: World Scientific Publishing Co. Pte. Ltd, 2021.
Game theory is the mathematical discipline aimed to model various interactions of living organisms in quantitative terms. Game theory, as the universal method for the analysis of social interactions has wide applications in economics, in the theory of control and management, financial mathematics, evolutionary biology, sociology, psychology and politics, in modelling different social processes, in ...
Added: October 29, 2021
Smirnov A., Starkov E., American Economic Journal: Microeconomics 2022 Vol. 14 No. 2 P. 506–560
Sellers often have the power to censor the reviews of their products. We explore the effect of these censorship policies in markets where some consumers are unaware of possible censorship. We find that if the share of such "naive" consumers is not too large, then rational consumers treat any bad review that is revealed in ...
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Piermont E., Zuazo-Garin P., / Series 2105 "[econ.TH]". 2021.
In dynamic settings each economic agent's choices can be revealing of her private information. This elicitation via the rationalization of observable behavior depends each agent's perception of which payoff-relevant contingencies other agents persistently deem as impossible. We formalize the potential heterogeneity of these perceptions as disagreements at higher-orders about the set of payoff states of ...
Added: October 5, 2021
Yeung D., Luckraz S., Leong C. K., Birkhäuser, 2020.
This contributed volume presents the state-of-the-art of games and dynamic games, featuring several chapters based on plenary sessions at the ISDG-China Chapter Conference on Dynamic Games and Game Theoretic Analysis, which was held from August 3-5, 2017 at the Ningbo campus of the University of Nottingham, China. The chapters in this volume will provide readers ...
Added: August 26, 2020
Blakeway S., Gromov D., Gromova E. et al., Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya 2019 Vol. 15 No. 1 P. 22–38
We describe a novel game-theoretic formulation of the optimal mobile agents’ placement problem which arises in the context of Mobile Ad-hoc Networks (MANETs). This problem is modelled as a sequential multistage game. The definitions of both the Nash equilibrium and cooperative solution are given. A modification was proposed to ensure the existence of a Nash ...
Added: March 13, 2020
Birkhauser/Springer, 2019.
This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on “Game Theory and Management” 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018. ...
Added: December 26, 2019
Andreev N. A., В кн.: "Тихоновские чтения": научная конференция: тезисы докладов: посвящается памяти академика Андрея Николаевича Тихонова: 29 октября-1 ноября 2019 г.: М.: ООО «Макс Пресс», 2019. С. 14–14.
Доклад посвящен приложению гарантированного подхода, предложенного Смирновым С.Н. [1],[2], к задаче управления портфелем финансовых инструментов на низколиквидном рынке с учетом модельной ошибки. Рассматривается игровая постановка в дискретном времени на конечном горизонте, в рамках которой инвестор максимизирует ожидаемое вознаграждение от портфеля (робастный эквивалент Сэвиджа) в конце стратегии. Оптимальная стратегия находится в неявном виде как решение соответствующего ...
Added: October 30, 2019
Andreev N. A., Mathematics 2019 Vol. 7 No. 12 P. 1147
We present a robust dynamic programming approach to the general portfolio selection problem in the presence of transaction costs and trading limits. We formulate the problem as a dynamic infinite game against nature and obtain the corresponding Bellman-Isaacs equation. Under~several additional assumptions, we get an alternative form of the equation, which is more feasible for ...
Added: October 30, 2019
Kuzyutin D., Gromova E., 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. ...
Added: October 8, 2019