Time-consistency of an imputation in a cooperative hybrid differential game

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Time-consistency of an imputation in a cooperative hybrid differential game. / Gromova, Ekaterina ; Zaremba, Anastasiia ; Su, Shimai.

In: Mathematics, Vol. 9, No. 15, 1830, 03.08.2021.

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

BibTeX

@article{6636a6142333467ea0fdea25d0284376,

title = "Time-consistency of an imputation in a cooperative hybrid differential game",

abstract = "This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.",

keywords = "Cooperative differential game, Dynamic programming principle, Hybrid differential game, Imputation distribution procedure, Random time horizon, Time-consistency, hybrid differential game, random time horizon, dynamic programming principle, INVESTMENT, cooperative differential game, imputation distribution procedure, CONSUMPTION, time-consistency",

author = "Ekaterina Gromova and Anastasiia Zaremba and Shimai Su",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = aug,

day = "3",

doi = "10.3390/math9151830",

language = "English",

volume = "9",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "15",

}

RIS

TY - JOUR

T1 - Time-consistency of an imputation in a cooperative hybrid differential game

AU - Gromova, Ekaterina

AU - Zaremba, Anastasiia

AU - Su, Shimai

PY - 2021/8/3

Y1 - 2021/8/3

N2 - This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.

AB - This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.

KW - Cooperative differential game

KW - Dynamic programming principle

KW - Hybrid differential game

KW - Imputation distribution procedure

KW - Random time horizon

KW - Time-consistency

KW - hybrid differential game

KW - random time horizon

KW - dynamic programming principle

KW - INVESTMENT

KW - cooperative differential game

KW - imputation distribution procedure

KW - CONSUMPTION

KW - time-consistency

UR - http://www.scopus.com/inward/record.url?scp=85112355654&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/71d62e23-9e5f-3b26-b988-49b801f558e1/

U2 - 10.3390/math9151830

DO - 10.3390/math9151830

M3 - Article

AN - SCOPUS:85112355654

VL - 9

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 15

M1 - 1830

ER -

ID: 85309501