Coalition and Anti-coalition Interaction in Cooperative Differential Games

Gromova, Ekaterina; Марова, Екатерина

doi:10.1016/j.ifacol.2018.11.466

Cited by 5 publications

(8 citation statements)

References 6 publications

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“…This paper extends and generalizes a number of results scattered through the series of works by the first author, [14,12,13]. See also [25,28] for related results.…”

Section: Introductionsupporting

confidence: 76%

“…While this result does not need to hold in general, it shows that there is a certain interconnection between different types of charateristic functions that is yet to be studied. This paper extends and generalizes a number of results scattered through the series of works by the first author, [14,12,13]. See also [25,28] for related results.…”

Section: Introductionsupporting

confidence: 75%

See 1 more Smart Citation

A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

Gromova¹,

Марова²,

Gromov³

2020

Journal of Dynamics &Amp; Games

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In this paper, we present a systematic overview of different endogenous optimization-based characteristic functions and discuss their properties. Furthermore, we define and analyze in detail a new, η-characteristic function. This characteristic function has a substantial advantage over other characteristic functions in that it can be obtained with a minimal computational effort and has a reasonable economic interpretation. In particular, the new characteristic function can be seen as a reduced version of the classical Neumann-Morgenstern characteristic function, where the players both from the coalition and from the complementary coalition use their previously computed strategies instead of solving respective optimization problems. Our finding are illustrated by a pollution control game with n non-identical players. For the considered game, we compute all characteristic functions and compare their properties. Quite surprisingly, it turns out that both the characteristic functions and the resulting cooperative solutions satisfy some symmetry relations.

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“…This paper extends and generalizes a number of results scattered through the series of works by the first author, [14,12,13]. See also [25,28] for related results.…”

Section: Introductionsupporting

confidence: 76%

Section: Introductionsupporting

confidence: 75%

A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

Gromova¹,

Марова²,

Gromov³

2020

Journal of Dynamics &Amp; Games

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show abstract

“…В работе [16] был предложен новый подход, а именно η-характеристическая функция, значения которой вычисляются следующим образом:…”

Section: постановка задачиunclassified

“…Марова рактеристических функций с целью упрощения вычислений в динамических играх, были предложены в работах [9], [24], [26] и др. В работах [5], [16] были предложены новые способы построения х.ф., которые затем были названы, соответственно, ζ-и η-характеристическими функциями. Отметим, что сильной стороной ζ-х.ф.…”

Section: Introductionunclassified

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Superadditive extension of characteristic functions for cooperative differential games

Громова¹,

Gromova²,

Марова³

2020

MGTA

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The paper provides a constructive theorem that allows one to construct a superadditive characteristic function in a differential game based on a non-superadditive one. As an example, a differential game is considered in which the delta - and eta - characteristic functions are not superadditive. An additional construction is carried out and it is shown that the obtained functions satisfy superadditivity

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A Pollution Control Problem for the Aluminum Production in Eastern Siberia: Differential Game Approach

Gromova¹,

Tur²,

Barsuk³

2022

Lecture Notes in Control and Information Sciences - Proceedings

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Coalition and Anti-coalition Interaction in Cooperative Differential Games

Cited by 5 publications

References 6 publications

A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

Superadditive extension of characteristic functions for cooperative differential games

A Pollution Control Problem for the Aluminum Production in Eastern Siberia: Differential Game Approach

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