A Differential Game with Random Time Horizon and Discontinuous Distribution
One class of differential games with random duration is considered. It is assumed that the duration of the game is a random variable with values from a given finite interval. The cumulative distribution function (CDF) of this random variable is assumed to be discontinuous with two jumps on the inter...
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| Format: | Article |
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2185 |
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| author | Anastasiia Zaremba Ekaterina Gromova Anna Tur |
| author_facet | Anastasiia Zaremba Ekaterina Gromova Anna Tur |
| author_sort | Anastasiia Zaremba |
| collection | DOAJ |
| description | One class of differential games with random duration is considered. It is assumed that the duration of the game is a random variable with values from a given finite interval. The cumulative distribution function (CDF) of this random variable is assumed to be discontinuous with two jumps on the interval. It follows that the player’s payoff takes the form of the sum of integrals with different but adjoint time intervals. In addition, the first interval corresponds to the zero probability of the game to be finished, which results in terminal payoff on this interval. The method of construction optimal solution for the cooperative scenario of such games is proposed. The results are illustrated by the example of differential game of investment in the public stock of knowledge. |
| first_indexed | 2024-03-10T14:14:13Z |
| format | Article |
| id | doaj.art-031c5f9c429b4c6ab3c1d4054c242882 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:14:13Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-031c5f9c429b4c6ab3c1d4054c2428822023-11-20T23:54:42ZengMDPI AGMathematics2227-73902020-12-01812218510.3390/math8122185A Differential Game with Random Time Horizon and Discontinuous DistributionAnastasiia Zaremba0Ekaterina Gromova1Anna Tur2Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St Petersburg, RussiaDepartment of Mathematics, St. Petersburg School of Physics, Mathematics, and Computer Science, National Research University Higher School of Economics (HSE), Soyuza Pechatnikov ul. 16, 190008 St. Petersburg, RussiaFaculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St Petersburg, RussiaOne class of differential games with random duration is considered. It is assumed that the duration of the game is a random variable with values from a given finite interval. The cumulative distribution function (CDF) of this random variable is assumed to be discontinuous with two jumps on the interval. It follows that the player’s payoff takes the form of the sum of integrals with different but adjoint time intervals. In addition, the first interval corresponds to the zero probability of the game to be finished, which results in terminal payoff on this interval. The method of construction optimal solution for the cooperative scenario of such games is proposed. The results are illustrated by the example of differential game of investment in the public stock of knowledge.https://www.mdpi.com/2227-7390/8/12/2185differential gamerandom time horizondiscontinuous cdfdynamic programming principleopen-loop strategiesoptimal investment |
| spellingShingle | Anastasiia Zaremba Ekaterina Gromova Anna Tur A Differential Game with Random Time Horizon and Discontinuous Distribution Mathematics differential game random time horizon discontinuous cdf dynamic programming principle open-loop strategies optimal investment |
| title | A Differential Game with Random Time Horizon and Discontinuous Distribution |
| title_full | A Differential Game with Random Time Horizon and Discontinuous Distribution |
| title_fullStr | A Differential Game with Random Time Horizon and Discontinuous Distribution |
| title_full_unstemmed | A Differential Game with Random Time Horizon and Discontinuous Distribution |
| title_short | A Differential Game with Random Time Horizon and Discontinuous Distribution |
| title_sort | differential game with random time horizon and discontinuous distribution |
| topic | differential game random time horizon discontinuous cdf dynamic programming principle open-loop strategies optimal investment |
| url | https://www.mdpi.com/2227-7390/8/12/2185 |
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