About one differential game with payment functions type of Germeier's convolution

Victor A. Gorelik^ab, Tatiana V. Zolotova<sup>c

a</sup> MPSU
^b FRC CSC RAS
^c Financial University under the Government of the Russian Federation

Abstract: The paper considers a differential game model with functionals that are a convolution of the minimum type of two criteria, one of which describes the competition of players in some general (external) sphere of activity, and the other describes the personal achievements of each player (in the internal sphere). The player control is the distribution of resources between the external and internal spheres. It is shown that under some natural assumptions of monotonicity of criteria in such games, Nash and Stackelberg equilibria exist and coincide, possessing the properties of stability and Pareto-optimality. This work is a development of the results for the static model published by the authors in this journal in 2022.

Keywords: differential game, Stackelberg equilibrium, Nash equilibrium, minimum convolutions, external sphere, internal sphere.

UDC: 519.834
BBK: 22.18

Received: 08.07.2024
Revised: 17.08.2024
Accepted: 01.12.2024