Multistage Games with Pairwise Interactions on Complete Graph

Bulgakova, Maria A.; Petrosyan, Leon A.

doi:10.1134/s0005117920080135

Cited by 4 publications

(4 citation statements)

References 4 publications

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“…In (Petrosyan and Bulgakova, 2015) and (Bulgakova, 2019), the star model is proposed, and the Shapley value formula is given to study its distribution of income. (Petrosyan and Bulgakova, 2020) is dedicated to the study of multi-stage games with pairwise interactions under the consideration of complete graphs, constructing characteristic functions, and calculating Shapley values. In (Bulgakova, 2019) and (Pankratova, 2018), studies on the construction of the characteristic function are carried out.…”

Section: Introductionmentioning

confidence: 99%

Cooperative Solutions in Multi-Star Network Games

Tian,

Jianpeng

2023

Contributions to Game Theory and Management

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A model also known as multi-agent systems, namely the multistar model is considered. In a multi-agent system, a two-level game is played, the first-level is the external game, and the second-level is the internal game. An approach is proposed how to distribute the benefits to players in the first-level game and the second-level game. The characteristic functions are constructed for the multi-star model. Based on the proposed characteristic functions, the combination of the Shapley value and the proportional solution as natural optimal principle to distribute the benefits in the first-level game and in the second-level game is proposed.

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Section: Introductionmentioning

confidence: 99%

Cooperative Solutions in Multi-Star Network Games

Tian,

Jianpeng

2023

Contributions to Game Theory and Management

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“…The following two types of games on graphs should be mentioned. In the first type of games on graphs, players move from one vertex of the graph to an adjacent vertex by jumping [31][32][33][34][35][36][37]. In the second type of games, players move along the edges of the graph [38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex

Азамов¹,

Ibragimov

Ibaydullaev

et al. 2021

Symmetry

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We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies.

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“…To the best of the author's knowledge, the research related to cooperative games with pairwise interaction is done in [4][5][6][7][8]. For the first time, in a cooperative form, a multistage network game with pairwise interaction is considered, when players play bimatrix games with their neighbors by network structure, and sufficient conditions for strong time consistency of the core are formulated [4].…”

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confidence: 99%

“…Furthermore, alternative approaches to constructing the characteristic function for games with pairwise interaction are considered [7]. And a new characteristic function is constructed, which has a lower computational complexity than the classical one, the IDP-core is proposed and its strong time consistency proved [8].…”

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confidence: 99%

A note on cooperative differential games with pairwise interactions

He,

Petrosyan

2024

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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In this paper, a differential game with pairwise interaction in a network is proposed. For explicitly, the vertices are players, and the edges are connections between them. Meanwhile, we consider the cooperative case. One special characteristic function is introduced and its convexity is proved. The core is used as a cooperative optimality principle. The characteristic function allows the construction of a time-consistent (dynamically stable) solutions, such as the Shapley value and the core. Finally, the results are illustrated by an example.

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Multistage Games with Pairwise Interactions on Complete Graph

Cited by 4 publications

References 4 publications

Cooperative Solutions in Multi-Star Network Games

Cooperative Solutions in Multi-Star Network Games

Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex

A note on cooperative differential games with pairwise interactions

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