| Autor: |
Nikolay A. Krasovskii, Alexander M. Tarasyev |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2020. |
| ISSN: |
0094-243X |
| DOI: |
10.1063/5.0049549 |
| Popis: |
The paper is devoted to analysis of stability properties of value functions in 2x3 dynamic bimatrix games. Stability properties at points of differentiability of value functions are expressed by Hamilton-Jacobi equations. There exist special domains in which value functions are not differentiable. In this case stability properties are verified basing on differential inequalities, particularly, on the basis of the apparatus of conjugate derivatives. For 2x3 dynamic bimatrix games with objective functionals on the infinite horizon smooth branches of value functions are constructed with the help of the method of generalized characteristics. It is show that smooth branches of the value functions are pasted together either smoothly or with the proper stability slopes in the non-smooth cases. Saddle points, Nash equilibria and switching surfaces are constructed for optimal control strategies for the game in the dynamic setting. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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