# Construction of Strongly Time-Consistent Subcores in Differential Games with Prescribed Duration

Результат исследований: Научные публикации в периодических изданияхстатья

### Выдержка

A new strongly time-consistent (dynamically stable) optimality principle is proposed in a cooperative differential game. This is done by constructing a special subset of the core of the game. It is proposed to consider this subset as a new optimality principle. The construction is based on the introduction of a function V that dominates the values of the classical characteristic function in coalitions. Suppose that V (S, x(t), T -t) is the value of the classical characteristic function computed in the subgame with initial conditions x(t), T -t on the cooperative trajectory. Define V (S; x0, T -t0) = max t0 = t= T V (S; x *(t), T -t) V (N; x *(t), T -t) V (N; x0, T -t0). Using this function, we construct an analog of the classical core. It is proved that the constructed core is a subset of the classical core; thus, we can consider it as a new optimality principle. It is also proved that the newly constructed optimality principle is strongly time-consistent.

Язык оригинала Английский S137-S144 8 Proceedings of the Steklov Institute of Mathematics 301 https://doi.org/10.1134/S0081543818050115 Опубликовано - июл 2018

### Цитировать

@article{fcb6408b94ce4a98916521fb63ae3d3b,
title = "Construction of Strongly Time-Consistent Subcores in Differential Games with Prescribed Duration",
abstract = "A new strongly time-consistent (dynamically stable) optimality principle is proposed in a cooperative differential game. This is done by constructing a special subset of the core of the game. It is proposed to consider this subset as a new optimality principle. The construction is based on the introduction of a function V that dominates the values of the classical characteristic function in coalitions. Suppose that V (S, x(t), T -t) is the value of the classical characteristic function computed in the subgame with initial conditions x(t), T -t on the cooperative trajectory. Define V (S; x0, T -t0) = max t0 = t= T V (S; x *(t), T -t) V (N; x *(t), T -t) V (N; x0, T -t0). Using this function, we construct an analog of the classical core. It is proved that the constructed core is a subset of the classical core; thus, we can consider it as a new optimality principle. It is also proved that the newly constructed optimality principle is strongly time-consistent.",
keywords = "cooperative differential game, strong time consistency, core, subcore, imputation",
author = "Petrosyan, {L. A.} and Панкратова, {Ярославна Борисовна}",
year = "2018",
month = "7",
doi = "10.1134/S0081543818050115",
language = "Английский",
volume = "301",
pages = "S137--S144",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "МАИК {"}Наука/Интерпериодика{"}",

}

В: Proceedings of the Steklov Institute of Mathematics, Том 301, 07.2018, стр. S137-S144.

Результат исследований: Научные публикации в периодических изданияхстатья

TY - JOUR

T1 - Construction of Strongly Time-Consistent Subcores in Differential Games with Prescribed Duration

AU - Petrosyan, L. A.

AU - Панкратова, Ярославна Борисовна

PY - 2018/7

Y1 - 2018/7

N2 - A new strongly time-consistent (dynamically stable) optimality principle is proposed in a cooperative differential game. This is done by constructing a special subset of the core of the game. It is proposed to consider this subset as a new optimality principle. The construction is based on the introduction of a function V that dominates the values of the classical characteristic function in coalitions. Suppose that V (S, x(t), T -t) is the value of the classical characteristic function computed in the subgame with initial conditions x(t), T -t on the cooperative trajectory. Define V (S; x0, T -t0) = max t0 = t= T V (S; x *(t), T -t) V (N; x *(t), T -t) V (N; x0, T -t0). Using this function, we construct an analog of the classical core. It is proved that the constructed core is a subset of the classical core; thus, we can consider it as a new optimality principle. It is also proved that the newly constructed optimality principle is strongly time-consistent.

AB - A new strongly time-consistent (dynamically stable) optimality principle is proposed in a cooperative differential game. This is done by constructing a special subset of the core of the game. It is proposed to consider this subset as a new optimality principle. The construction is based on the introduction of a function V that dominates the values of the classical characteristic function in coalitions. Suppose that V (S, x(t), T -t) is the value of the classical characteristic function computed in the subgame with initial conditions x(t), T -t on the cooperative trajectory. Define V (S; x0, T -t0) = max t0 = t= T V (S; x *(t), T -t) V (N; x *(t), T -t) V (N; x0, T -t0). Using this function, we construct an analog of the classical core. It is proved that the constructed core is a subset of the classical core; thus, we can consider it as a new optimality principle. It is also proved that the newly constructed optimality principle is strongly time-consistent.

KW - cooperative differential game

KW - strong time consistency

KW - core

KW - subcore

KW - imputation

U2 - 10.1134/S0081543818050115

DO - 10.1134/S0081543818050115

M3 - статья

VL - 301

SP - S137-S144

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

ER -