Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game
This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an <i>n</i>-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/15/1830 |
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| author | Ekaterina Gromova Anastasiia Zaremba Shimai Su |
| author_facet | Ekaterina Gromova Anastasiia Zaremba Shimai Su |
| author_sort | Ekaterina Gromova |
| collection | DOAJ |
| description | This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an <i>n</i>-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations. |
| first_indexed | 2024-03-10T09:11:46Z |
| format | Article |
| id | doaj.art-201efaf0c7274901a76987f69a70e6ce |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:11:46Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-201efaf0c7274901a76987f69a70e6ce2023-11-22T05:57:19ZengMDPI AGMathematics2227-73902021-08-01915183010.3390/math9151830Time-Consistency of an Imputation in a Cooperative Hybrid Differential GameEkaterina Gromova0Anastasiia Zaremba1Shimai Su2Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, RussiaFaculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, RussiaFaculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, RussiaThis work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an <i>n</i>-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.https://www.mdpi.com/2227-7390/9/15/1830hybrid differential gamecooperative differential gamerandom time horizondynamic programming principleimputation distribution proceduretime-consistency |
| spellingShingle | Ekaterina Gromova Anastasiia Zaremba Shimai Su Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game Mathematics hybrid differential game cooperative differential game random time horizon dynamic programming principle imputation distribution procedure time-consistency |
| title | Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game |
| title_full | Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game |
| title_fullStr | Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game |
| title_full_unstemmed | Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game |
| title_short | Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game |
| title_sort | time consistency of an imputation in a cooperative hybrid differential game |
| topic | hybrid differential game cooperative differential game random time horizon dynamic programming principle imputation distribution procedure time-consistency |
| url | https://www.mdpi.com/2227-7390/9/15/1830 |
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