A substitute for the classical neumann-morgenstern characteristic function in cooperative differential games

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A substitute for the classical neumann-morgenstern characteristic function in cooperative differential games. / Gromova, Ekaterina ; Marova, Ekaterina ; Gromov, Dmitry.

In: Journal of Dynamics and Games, Vol. 7, No. 2, 01.04.2020, p. 105-122.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{b71e82e70f3d4aabb1548efa758ae62b,

title = "A substitute for the classical neumann-morgenstern characteristic function in cooperative differential games",

abstract = "In this paper, we present a systematic overview of diffierent endogenous optimization-based characteristic functions and discuss their properties. Furthermore, we define and analyze in detail a new, n-characteristic function. This characteristic function has a substantial advantage over other characteristic functions in that it can be obtained with a minimal computational effiort 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.",

keywords = "Characteristic function, Cooperative games, Diffierential games, Pollution control, COALITION, pollution control, differential games, ALLOCATION, characteristic function",

author = "Ekaterina Gromova and Ekaterina Marova and Dmitry Gromov",

note = "Publisher Copyright: {\textcopyright} 2020, American Institute of Mathematical Sciences.",

year = "2020",

month = apr,

day = "1",

doi = "10.3934/jdg.2020007",

language = "English",

volume = "7",

pages = "105--122",

journal = "Journal of Dynamics and Games",

issn = "2164-6066",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

RIS

TY - JOUR

T1 - A substitute for the classical neumann-morgenstern characteristic function in cooperative differential games

AU - Gromova, Ekaterina

AU - Marova, Ekaterina

AU - Gromov, Dmitry

PY - 2020/4/1

Y1 - 2020/4/1

N2 - In this paper, we present a systematic overview of diffierent endogenous optimization-based characteristic functions and discuss their properties. Furthermore, we define and analyze in detail a new, n-characteristic function. This characteristic function has a substantial advantage over other characteristic functions in that it can be obtained with a minimal computational effiort 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.

AB - In this paper, we present a systematic overview of diffierent endogenous optimization-based characteristic functions and discuss their properties. Furthermore, we define and analyze in detail a new, n-characteristic function. This characteristic function has a substantial advantage over other characteristic functions in that it can be obtained with a minimal computational effiort 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.

KW - Characteristic function

KW - Cooperative games

KW - Diffierential games

KW - Pollution control

KW - COALITION

KW - pollution control

KW - differential games

KW - ALLOCATION

KW - characteristic function

UR - http://www.scopus.com/inward/record.url?scp=85086171622&partnerID=8YFLogxK

U2 - 10.3934/jdg.2020007

DO - 10.3934/jdg.2020007

M3 - Article

AN - SCOPUS:85086171622

VL - 7

SP - 105

EP - 122

JO - Journal of Dynamics and Games

JF - Journal of Dynamics and Games

SN - 2164-6066

IS - 2

ER -

ID: 53985967