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

  • Victor A. Gorelik FRC CSC RAS, MPSU
  • Виктор Александрович Горелик FRC CSC RAS, MPSU
  • Tatiana V. Zolotova Financial University under the Government of the Russian Federation
  • Татьяна Валерьяновна Золотова Financial University under the Government of the Russian Federation
DOI: https://doi.org/10.17076/mgta_2024_4_86
Keywords: differential game, Stackelberg equilibrium, Nash equilibrium, minimum convolutions, external sphere, internal sphere

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.

Published
2024-12-06
How to Cite
Gorelik, V., Горелик, В., Zolotova, T., & Золотова, Т. (2024). About one differential game with payment functions type of Germeier’s convolution. Mathematical Game Theory and Applications, 16(4), 3-20. https://doi.org/10.17076/mgta_2024_4_86
Issue
Vol 16 No 4 (2024): Mathematical game theory and applications
Section
Статьи
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