On the Estimation of the Initial Stock in the Problem of Resource Extraction
We consider a differential game of non-renewable resource extraction, in which the players do not know the precise value of the resource stock and, thus, have to make an estimate. We define the value of information about the initial stock and give recommendations for the choice of the estimate depen...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/23/3099 |
| _version_ | 1797507422119526400 |
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| author | Anna Tur Ekaterina Gromova Dmitry Gromov |
| author_facet | Anna Tur Ekaterina Gromova Dmitry Gromov |
| author_sort | Anna Tur |
| collection | DOAJ |
| description | We consider a differential game of non-renewable resource extraction, in which the players do not know the precise value of the resource stock and, thus, have to make an estimate. We define the value of information about the initial stock and give recommendations for the choice of the estimate depending on the parameters of the problem. Further, we consider the situation where the players only know the bounds for the stock of the resource and solve the problem of computing the optimal estimate, such that it minimizes the players’ losses in the worst-case scenario. The analysis allows us to give a simple rule for the choice of the optimal estimate of the resource stock. |
| first_indexed | 2024-03-10T04:48:16Z |
| format | Article |
| id | doaj.art-489facdc8bf94a5297509758f4b214aa |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T04:48:16Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-489facdc8bf94a5297509758f4b214aa2023-11-23T02:46:02ZengMDPI AGMathematics2227-73902021-12-01923309910.3390/math9233099On the Estimation of the Initial Stock in the Problem of Resource ExtractionAnna Tur0Ekaterina Gromova1Dmitry Gromov2Faculty of Applied Mathematics and Control Processes, St Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, RussiaFaculty of Applied Mathematics and Control Processes, St Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, RussiaFaculty of Applied Mathematics and Control Processes, St Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, RussiaWe consider a differential game of non-renewable resource extraction, in which the players do not know the precise value of the resource stock and, thus, have to make an estimate. We define the value of information about the initial stock and give recommendations for the choice of the estimate depending on the parameters of the problem. Further, we consider the situation where the players only know the bounds for the stock of the resource and solve the problem of computing the optimal estimate, such that it minimizes the players’ losses in the worst-case scenario. The analysis allows us to give a simple rule for the choice of the optimal estimate of the resource stock.https://www.mdpi.com/2227-7390/9/23/3099differential gamecooperative solutionimperfect informationvalue of informationnon-renewable resource extraction |
| spellingShingle | Anna Tur Ekaterina Gromova Dmitry Gromov On the Estimation of the Initial Stock in the Problem of Resource Extraction Mathematics differential game cooperative solution imperfect information value of information non-renewable resource extraction |
| title | On the Estimation of the Initial Stock in the Problem of Resource Extraction |
| title_full | On the Estimation of the Initial Stock in the Problem of Resource Extraction |
| title_fullStr | On the Estimation of the Initial Stock in the Problem of Resource Extraction |
| title_full_unstemmed | On the Estimation of the Initial Stock in the Problem of Resource Extraction |
| title_short | On the Estimation of the Initial Stock in the Problem of Resource Extraction |
| title_sort | on the estimation of the initial stock in the problem of resource extraction |
| topic | differential game cooperative solution imperfect information value of information non-renewable resource extraction |
| url | https://www.mdpi.com/2227-7390/9/23/3099 |
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