Construction of strongly time-consistent subcores in differential games with prescribed duration

L. A. Petrosyan ; Ya. B. Pankratova

Trudy Instituta matematiki i mehaniki, Tome 23 (2017) no. 1, pp. 219-227

Résumé

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 $\hat{V}$ that dominates the values of the classical characteristic function in coalitions. Suppose that $V(S,\bar{x}(\tau),T-\tau)$ is the value of the classical characteristic function computed in the subgame with initial conditions $\bar{x}(\tau)$, $T-\tau$ on the cooperative trajectory. Define $$\hat{V}(S;x_0,T-t_0)=\displaystyle\max_{t_0\leq \tau\leq T}\frac{V(S;x^*(\tau),T-\tau)}{V(N;x^*(\tau),T-\tau)}V(N;x_0,T-t_0).$$ 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.

Détail

Keywords: cooperative differential game, strong time consistency, subcore
Mots-clés : core, imputation.