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 ˆV that dominates the values of the classical characteristic function in coalitions. Suppose that V(S,ˉx(τ),T−τ) is the value of the classical characteristic function computed in the subgame with initial conditions ˉx(τ), T−τ on the cooperative trajectory. Define ˆV(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:
cooperative differential game, strong time consistency, core, subcore, imputation.
Citation:
L. A. Petrosyan, Ya. B. Pankratova, “Construction of strongly time-consistent subcores in differential games with prescribed duration”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 1, 2017, 219–227; Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 137–144