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Formation of Coalition Structures as a Non-Cooperative Game
Levando D. V.
Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This paper suggests an approach to this problem in the framework of a noncooperative game theory. Definition of a suggested finite game includes a family of nested simultaneous non-cooperative finite games with intra- and inter-coalition externalities. In this family, games differ by the size of maximum coalition, partitions and by coalition structure formation rules. A result of every game consists of partition of players into coalitions and a payoff profile for every player. Every game in the family has an equilibrium in mixed strategies with possibly more than one coalition. The results of the game differ from those conventionally discussed in cooperative game theory, e.g. the Shapley value, strong Nash, coalition-proof equilibrium, core, kernel, nucleolus. We discuss the following applications of the new game: cooperation as an allocation in one coalition, Bayesian games, stochastic games and construction of a non-cooperative criterion of coalition structure stability for studying focal points.
Hermida Rivera H., Public Choice 2025 Vol. 203 P. 493–501
This note shows that under the unrestricted domain, there exists a choice liberal and Nash implementable social choice rule if and only if there are at least three players and the outcome set is at least twice as large as the player set. A social choice rule is choice liberal if and only if for ...
Added: September 22, 2026
Boros E., Elbassioni K., Gurvich V. et al., Dynamic Games and Applications 2026 Vol. 16 P. 1097–1115
We prove that every finite two-person shortest path game, where the local cost of every move is positive for each player, has a Nash equilibrium (NE) in pure stationary strategies, which can be computed in polynomial time. We also extend the existence result to infinite graphs with finite outdegrees. Moreover, our proof gives that a ...
Added: February 22, 2026
Kemgne M. W., Njionou B. B., Ignatov D. I. et al., International Journal of Approximate Reasoning 2025 Vol. 186 Article 109527
This paper introduces cooperative games with transferable utilities and fuzzy characteristic functions on concept lattices. While previous works have independently addressed games with fuzzy payoffs and games restricted to structured coalition systems such as lattices, our approach combines both perspectives. We consider cooperative settings where coalition formation is constrained by a concept lattice structure, and ...
Added: January 23, 2026
Cham: Birkhäuser, 2024.
This book collects a selection of the articles presented at the virtual conference “Game Theory and Applications”, organized in St. Petersburg in the summer of 2022. The articles in this collection cover all the main applications of game theory, interpolating mathematical methods with economics, biology, sociology, mobile systems, and social networks. Scholars in the field ...
Added: May 21, 2025
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
Pankratova Y., Petrosyan L., , in: Stability and Control Processes: Proceedings of the 4th International Conference Dedicated to the Memory of Professor Vladimir Zubov.: Cham: Springer, 2022. Ch. 65 P. 447–455.
Added: June 5, 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
Cham: Birkhäuser, 2021.
This book features contributions from the GTM 2020 International Meeting on Game Theory held virtually from St. Petersburg, Russia, including presentations by plenary speakers. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management. ...
Added: April 5, 2022
Shevchenko V., Логико-философские штудии 2021 Vol. 19 No. 2 P. 131–135
The paper sketches a way to connect the cognitively realistic notion of relevance needed for social coordination and game-theoretic models of such coordination, in particular, that of correlated equilibrium. Such a connection would help to answer the question of how social coordination described in game theory is evolutionary and cognitively possible. The main argument put ...
Added: October 5, 2021
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
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