Построение сильно-динамически устойчивых подъядер в дифференциальных играх с предписанной продолжительностью

Труды института математики и механики УрО РАН. 2017. Т. 23. № 1. С. 219–227.

Pankratova Y., Петросян Л. А.

   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 ^  V^ that dominates the values of the classical characteristic function in coalitions. Suppose that V(S,x ¯ (τ),T−τ) V(S,x¯(τ),T−τ) is the value of the classical characteristic function computed in the subgame with initial conditions x ¯ (τ) x¯(τ) , T−τ T−τ on the cooperative trajectory. Define

V ^ (S;x 0 ,T−t 0 )=max t 0 ≤τ≤T V(S;x ∗ (τ),T−τ)V(N;x ∗ (τ),T−τ) V(N;x 0 ,T−t 0 ). 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 proved also that the newly constructed optimality principle is strongly time-consistent.

Keywords: core, c-ядро, Strong time consistency, cooperative differential game, subcore, сильно-динамическая устойчивость, кооперативная дифференциальная игра, подъядро