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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2017 Volume 23, Number 1, Pages 219–227 (Mi timm1397)

This article is cited in 3 papers

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

L. A. Petrosyan, Ya. B. Pankratova

Saint Petersburg State University

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 $\hat{V}$ 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.

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

UDC: 517.977

MSC: 37C75

Received: 30.10.2016

DOI: 10.21538/0134-4889-2017-23-1-219-227


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2018, 301, suppl. 1, 137–144

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