Cooperative Optimality Principles in Differential Games on Networks

Tur, Anna; Petrosyan, Leon A.

doi:10.1134/s0005117921060096

Cited by 4 publications

(2 citation statements)

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“…Later, (Petersyan and Yeung, 2020) proposed a new characteristic function, which satisfies the convexity property. In the paper (Tur and Petrosyan, 2021) some basic solutions are investigated, such as Core, The Shapley value (Shapley, 1953) and τ −value (Tijs, 1987). , a new characteristic function combined with the partner set is constructed.…”

Section: Introductionmentioning

confidence: 99%

Cooperative Differential Games with Pairwise Interactions in Pollution Control Problems

2023

Contributions to Game Theory and Management

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This paper establishes a new class of dynamic games which contain two phenomena often observed in real-life, differential network games and pairwise interactions. It is assumed that the vertices of the network are players, and the edges are connections between them. By cooperation, a particular type of characteristic function is introduced. Then, the cooperative solutions are constructed, proportional solution and the Shapley value. Finally, the results are illustrated by an example.

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Section: Introductionmentioning

confidence: 99%

Cooperative Differential Games with Pairwise Interactions in Pollution Control Problems

2023

Contributions to Game Theory and Management

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“…A time-consistent Shapley value and τ value solution in a class of differential network games was proposed in [13]. Later, Tur and Petrosyan give a simplified formula for the calculation of the Shapley value [14]. Additionally, they also proved that the core is strongly time-consistent [15].…”

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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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