### 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 |
---|---|

Страницы (с-по) | S137-S144 |

Число страниц | 8 |

Журнал | Proceedings of the Steklov Institute of Mathematics |

Том | 301 |

DOI | |

Состояние | Опубликовано - июл 2018 |

### Цитировать

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**Construction of Strongly Time-Consistent Subcores in Differential Games with Prescribed Duration.** / Petrosyan, L. A.; Панкратова, Ярославна Борисовна.

Результат исследований: Научные публикации в периодических изданиях › статья

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 -