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¯ (τ), T −τ) is the value of the classical characteristic function computed in the subgame with initial conditions x¯ (τ), T −τ on the cooperative trajectory. Define V^(S;X0,T−t0)=maxt0≤τ≤TV(S;x∗(τ),T−τ)V(N;X∗(τ),T−τ)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¯ (τ), T −τ) is the value of the classical characteristic function computed in the subgame with initial conditions x¯ (τ), T −τ on the cooperative trajectory. Define V^(S;X0,T−t0)=maxt0≤τ≤TV(S;x∗(τ),T−τ)V(N;X∗(τ),T−τ)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

UR - http://www.scopus.com/inward/record.url?scp=85051712353&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/construction-strongly-timeconsistent-subcores-differential-games-prescribed-duration

U2 - 10.1134/S0081543818050115

DO - 10.1134/S0081543818050115

M3 - статья

VL - 301

SP - 137

EP - 144

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

ER -