TY - JOUR

T1 - On the estimation of the switching moment of utility functions in cooperative differential games

AU - Е, Пэйчэнь

AU - Тур, Анна Викторовна

AU - Ву, Ийлунь

PY - 2024/11/1

Y1 - 2024/11/1

N2 - Purpose: The purpose of this paper is to emphasize that it is necessary to consider possible “switches” when constructing dynamic models. We consider a class of differential games with switching utility functions. Design/methodology/approach: We assume that the players do not have exact information about the switching moments. The problem is to compute the optimal estimate of the unknown such moment that minimizes the players’ losses in the worst case. Two scenarios are considered: (1) the players have the same estimate and (2) the players have different estimates of the switching moment. An example of an investment problem is given, and optimal controls and trajectories are calculated analytically using Pontryagin’s maximum principle. Findings: The analysis provides a simple rule for choosing the optimal estimate. It is shown that the players’ optimal estimates are identical in both scenarios. Originality/value: To date, no research has addressed the optimal estimation of uncertainty switching moments in a two-player differential game involving utility function switching. Our study offers detailed estimates of switching moments in the cooperative case. This allows players to thoroughly evaluate the performance of various estimated switching times and make well-informed conclusions.

AB - Purpose: The purpose of this paper is to emphasize that it is necessary to consider possible “switches” when constructing dynamic models. We consider a class of differential games with switching utility functions. Design/methodology/approach: We assume that the players do not have exact information about the switching moments. The problem is to compute the optimal estimate of the unknown such moment that minimizes the players’ losses in the worst case. Two scenarios are considered: (1) the players have the same estimate and (2) the players have different estimates of the switching moment. An example of an investment problem is given, and optimal controls and trajectories are calculated analytically using Pontryagin’s maximum principle. Findings: The analysis provides a simple rule for choosing the optimal estimate. It is shown that the players’ optimal estimates are identical in both scenarios. Originality/value: To date, no research has addressed the optimal estimation of uncertainty switching moments in a two-player differential game involving utility function switching. Our study offers detailed estimates of switching moments in the cooperative case. This allows players to thoroughly evaluate the performance of various estimated switching times and make well-informed conclusions.

KW - Differential game

KW - Minimax problems

KW - Optimal estimate switching moments

KW - Utility function switching

UR - https://www.mendeley.com/catalogue/6122bd53-ac75-3195-93c5-e086b9da9346/

U2 - 10.1108/k-05-2024-1241

DO - 10.1108/k-05-2024-1241

M3 - Article

JO - Kybernetes

JF - Kybernetes

SN - 0368-492X

ER -