TY - JOUR

T1 - Transferable utility cooperative differential games with continuous updating using pontryagin maximum principle

AU - Zhou, Jiangjing

AU - Tur, Anna

AU - Petrosian, Ovanes

AU - Gao, Hongwei

N1 - Funding Information: Funding: This work is supported by Postdoctoral International Exchange Program of China and funded by the Russian Foundation for Basic Research (RFBR) according to the Grant No. 18-00-00727 (18-00-00725), and the National Natural Science Foundation of China (Grant No. 71571108). Funding Information: Acknowledgments: The corresponding author would like to acknowledge the support from the China-Russia Operations Research and Management Cooperation Research Center, that is an association between Qingdao University and St. Petersburg State University. Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/14

Y1 - 2021/1/14

N2 - We consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interval of a fixed duration. Over time, information about the game structure will be updated. The subject of the current paper is to construct players’ cooperative strategies, their cooperative trajectory, the characteristic function, and the cooperative solution for this class of differential games with continuous updating, particularly by using Pontryagin’s maximum principle as the optimality conditions. In order to demonstrate this method’s novelty, we propose to compare cooperative strategies, trajectories, characteristic functions, and corresponding Shapley values for a classic (initial) differential game and a differential game with continuous updating. Our approach provides a means of more profound modeling of conflict controlled processes. In a particular example, we demonstrate that players’ behavior is braver at the beginning of the game with continuous updating because they lack the information for the whole game, and they are “intrinsically time-inconsistent”. In contrast, in the initial model, the players are more cautious, which implies they dare not emit too much pollution at first.

AB - We consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interval of a fixed duration. Over time, information about the game structure will be updated. The subject of the current paper is to construct players’ cooperative strategies, their cooperative trajectory, the characteristic function, and the cooperative solution for this class of differential games with continuous updating, particularly by using Pontryagin’s maximum principle as the optimality conditions. In order to demonstrate this method’s novelty, we propose to compare cooperative strategies, trajectories, characteristic functions, and corresponding Shapley values for a classic (initial) differential game and a differential game with continuous updating. Our approach provides a means of more profound modeling of conflict controlled processes. In a particular example, we demonstrate that players’ behavior is braver at the beginning of the game with continuous updating because they lack the information for the whole game, and they are “intrinsically time-inconsistent”. In contrast, in the initial model, the players are more cautious, which implies they dare not emit too much pollution at first.

KW - Cooperative differential game

KW - Differential games with continuous updating

KW - Hamiltonian

KW - Open-loop Nash equilibrium

KW - Pontryagin maximum principle

KW - δ-characteristic function

UR - http://www.scopus.com/inward/record.url?scp=85099993846&partnerID=8YFLogxK

U2 - 10.3390/math9020163

DO - 10.3390/math9020163

M3 - Article

AN - SCOPUS:85099993846

VL - 9

SP - 1

EP - 22

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 2

M1 - 163

ER -