On the superadditivity of a characteristic function in cooperative differential games with negative externalities

Gromova, Ekaterina; Malakhova, Anastasiya; Марова, Екатерина

doi:10.1109/cnsa.2017.7973963

Cited by 4 publications

(9 citation statements)

References 4 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%

“…In [26] it was proved that the δ-characterisctic function is superadditive for a certain class of static games if some conditions on the payoff function are fulfilled. However, in a general case the δ-characteristic function can turn out to be not superadditive as the recent result shows [12].…”

Section: δ-Characteristic Functionmentioning

confidence: 90%

See 2 more Smart Citations

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%

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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“…(2.5) Пример дифференциальной игры, для которой δ-х.ф. не является супераддитивной приведен в работе [15].…”

Section: постановка задачиunclassified

“…является супераддитивной функцией для некоторого достаточно широкого класса однократных игр [27], однако для динамической постановки существует ряд контрпримеров (см. [15], а также раздел 3.3.2 данной статьи). В данной работе в разделе 2 предлагается конструктивный способ построения супераддитивной характеристической функции на основе любой другой (несупераддитивной) характеристической функции.…”

Section: Introductionunclassified

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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Coalition and Anti-coalition Interaction in Cooperative Differential Games

Gromova

Марова

2018

IFAC-PapersOnLine

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On the superadditivity of a characteristic function in cooperative differential games with negative externalities

Cited by 4 publications

References 4 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

Coalition and Anti-coalition Interaction in Cooperative Differential Games

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