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On Nash Equilibrium in Repeated Hierarchical Games
Ch. 65. P. 447–455.
Pankratova Y., Petrosyan L.
Gurvich V., Naumova M., / Series "Working papers by Cornell University". 2024.
In several recent papers some concepts of convex analysis were extended to discrete sets. This paper is one more step in this direction. It is well known that a local minimum of a convex function is always its global minimum. We study some discrete objects that share this property and provide several examples of convex ...
Added: August 19, 2024
Gurvich V., Naumova M., Annals of Operations Research 2023 No. 336 P. 1905–1927
Added: August 7, 2024
Филатов А. Ю., / Series 02:43:16 "CEST". 2023.
The paper proposes a game theory model of price oligopoly with a heterogeneous product, where total demand depends linearly on the minimum market price. This model develops the Bertrand oligopoly for the case of imperfect price elasticity of demand. The most interesting result is an asymmetric Nash equilibrium with different prices and sales in the ...
Added: January 10, 2024
Boros E., Franciosa P. G., Gurvich V. et al., International Journal of Game Theory 2024 Vol. 53 P. 449–473
We prove that a deterministic n-person shortest path game has a Nash equlibrium in
pure and stationary strategies if it is edge-symmetric (that is (u, v) is a move whenever (v, u) is, apart from moves entering terminal vertices) and the length of every
move is positive for each player. Both conditions are essential, though it remains ...
Added: October 31, 2023
Gurvich V., Naumova M., Discrete Applied Mathematics 2023 Vol. 340 P. 53–68
In 1975 the first author proved that every finite tight two-person game form g is Nashsolvable,
that is, for every payoffs u and w of two players the obtained normal form game
(g; u,w) has a Nash equilibrium (NE) in pure strategies. Several proofs of this theorem
were obtained later. Here we strengthen the result and give a ...
Added: September 8, 2023
Samoylenko I., Кулешов И. В., Райгородский А. М., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 355–368
At the middle of the 2000-th, scientists studying the functioning of insect communities identified four basic patterns of the organizational structure of such communities. (i) Cooperation is more developed in groups with strong kinship. (ii) Cooperation in species with large colony sizes is often more developed than in species with small colony sizes. And small-sized ...
Added: July 28, 2023
Korolev A. V., Ougolnitsky G. A., International Game Theory Review 2023 Vol. 25 No. 2 Article 2350004
In this paper, we build and investigate cooperative games with different characteristic
functions (von Neumann–Morgenstern, Petrosyan–Zaccour, Gromova–Petrosyan) on the
base of symmetrical Cournot oligopoly game-theoretic models in normal form. We find
Nash and Stackelberg equilibria and cooperative solutions for nonsymmetrical Cournot
oligopoly game-theoretic models in normal form. Also, we build and investigate coop27
erative three-player games with the same characteristic ...
Added: January 26, 2023
Gurvich V., Naumova M., Annals of Mathematics and Artificial Intelligence 2022
We prove a new property of dual hypergraphs and derive from it Nash-solvability of the corresponding (tight) game forms. This result is known since 1975, but its new proof is much simpler. ...
Added: December 10, 2022
Korolev A. V., Automation and Remote Control 2022 Vol. 13 No. 1 P. 483–501
Stochastic parameters are introduced into a model of network games with production and knowledge externalities. The model was formulated by V. Matveenko and A. Korolev and generalizes Romer’s two-period model. The agents’ productivities have both deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle that ...
Added: April 22, 2022
Korolev A. V., Математическая теория игр и ее приложения 2021 № 1 С. 102–129
In this paper, stochastic parameters are introduced into the network games model with production and knowledges externalities. This model was formulated by V. Matveenko and A. Korolev and generalized two-period Romer model. Agents' productivities have deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle which ...
Added: May 15, 2021
Afanasiev V., Semion A., Проблемы управления 2021 № 1 С. 24–35
A differential game of several players is considered as follows. One player (attacker) penetrates some space, and several other players (pursuers) appear simultaneously to intercept the attacker. Upon detecting the pursuers, the attacker tries to evade them. The dynamics of each player are described by a time-invariant linear system of a general type with scalar ...
Added: April 6, 2021
Averboukh Y., Journal of Dynamical and Control Systems 2015 Vol. 21 No. 3 P. 329–350
The paper is concerned with a two-player nonzero-sum differential game in the case when players are informed about the current position. We consider the game in control with guide strategies first proposed by Krasovskii and Subbotin. The construction of universal strategies is given both for the case of continuous and discontinuous value functions. The existence ...
Added: April 22, 2020
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
Matveenko V., Garmash M., Korolev A. V., , in: Frontiers of Dynamic Games, Game Theory and Management, St. Petersburg, 2018.: Birkhäuser, 2019. Ch. 9 P. 157–174.
We study game equilibria in a model of production and externalities
in network with two types of agents who possess different productivities. Each
agent may invest a part of her endowment (for instance, time or money) on the
first stage; consumption on the second period depends on her own investment
and productivity as well as on the investments of ...
Added: October 30, 2019
Pankratova Y., Petrosyan L., В кн.: Lecture Notes in Computer ScienceVol. 11548.: Springer, 2019. С. 685–696.
In the paper, a two-level infinitely repeated hierarchical game with one player (center) C0 on the first level and S1...Sn subordinate players on the second is considered. On each stage of the game player C0 selects vector x=(x1....xn) from a given set X, in which each component represents a vector of resources delivered by C0 to one of the ...
Added: October 26, 2019
Kuchkarov I., Petrosian O., , in: Mathematical Optimization Theory and Operations Research, 18th International Conference, MOTOR 2019 Ekaterinburg, Russia, July 8–12, 2019Vol. 11548.: Springer, 2019. P. 635–650.
The subject of this paper is a linear quadratic case of a differential game model with continuous updating. This class of differential games is essentially new, there it is assumed that at each time instant, players have or use information about the game structure defined on a closed time interval with a fixed duration. As ...
Added: October 22, 2019
Pankratova Y., Петросян Л. А., Lecture Notes in Computer Science 2019 Vol. 11548 P. 685–696
In the paper, a two-level infinitely repeated hierarchical game with one player (center) C0 on the first level and S1...Sn subordinate players on the second is considered. On each stage of the game player C0 selects vector x=(x1....xn) from a given set X, in which each component represents a vector of resources delivered by C0 to one of the ...
Added: October 5, 2019
Networks Structure, Equilibria, and Adjustment Dynamics in Network Games with Nonhomogeneous Players
Гармаш М. В., Уткина А. А., Korolev A. V., , in: Contributions to Game Theory and Management Volume XIIVol. XII.: ., 2019. P. 128–139.
In this paper, we consider the following problem - what affects
the Nash equilibrium amount of investment in knowledge when some agents
of the complete graph enter another full one. The solution of this problem will
allow us to understand exactly how game agents will behave when deciding
whether to enter the other net, what conditions and externalities affect it
and ...
Added: September 29, 2019
., 2019.
In this paper, we consider the following problem - what affects
the Nash equilibrium amount of investment in knowledge when some agents
of the complete graph enter another full one. The solution of this problem will
allow us to understand exactly how game agents will behave when deciding
whether to enter the other net, what conditions and externalities affect it
and ...
Added: September 29, 2019
Korolev A. V., Garmashov I., , in: Optimization of Complex Systems: Theory, Models, Algorithms and Applications.: Switzerland: Springer Publishing Company, 2020. P. 398–406.
In this paper, we consider the following problem - what affects the Nash equilibrium amount of investment in knowledge when one of the complete graph enters another full one. The solution of this problem will allow us to understand exactly how game agents will behave when deciding whether to enter the other net, what conditions ...
Added: June 23, 2019
Switzerland: Springer Publishing Company, 2020.
In this paper, we consider the following problem - what affects the Nash equilibrium amount of investment in knowledge when one of the complete graph enters another full one. The solution of this problem will allow us to understand exactly how game agents will behave when deciding whether to enter the other net, what conditions ...
Added: June 23, 2019