Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle
We consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interval of a fixed duration. Over time, information abo...
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| Format: | Article |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/2/163 |
| _version_ | 1797411650416934912 |
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| author | Jiangjing Zhou Anna Tur Ovanes Petrosian Hongwei Gao |
| author_facet | Jiangjing Zhou Anna Tur Ovanes Petrosian Hongwei Gao |
| author_sort | Jiangjing Zhou |
| collection | DOAJ |
| description | We consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interval of a fixed duration. Over time, information about the game structure will be updated. The subject of the current paper is to construct players’ cooperative strategies, their cooperative trajectory, the characteristic function, and the cooperative solution for this class of differential games with continuous updating, particularly by using Pontryagin’s maximum principle as the optimality conditions. In order to demonstrate this method’s novelty, we propose to compare cooperative strategies, trajectories, characteristic functions, and corresponding Shapley values for a classic (initial) differential game and a differential game with continuous updating. Our approach provides a means of more profound modeling of conflict controlled processes. In a particular example, we demonstrate that players’ behavior is braver at the beginning of the game with continuous updating because they lack the information for the whole game, and they are “intrinsically time-inconsistent”. In contrast, in the initial model, the players are more cautious, which implies they dare not emit too much pollution at first. |
| first_indexed | 2024-03-09T04:49:12Z |
| format | Article |
| id | doaj.art-c4903c95242948bfa86e1ee4cd9fa0f4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:49:12Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c4903c95242948bfa86e1ee4cd9fa0f42023-12-03T13:12:23ZengMDPI AGMathematics2227-73902021-01-019216310.3390/math9020163Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum PrincipleJiangjing Zhou0Anna Tur1Ovanes Petrosian2Hongwei Gao3School of Mathematics and Statistics, Qingdao University, Qingdao 266071, ChinaSt. Petersburg State University, 7/9, Universitetskaya nab., St. Petersburg 199034, RussiaSchool of Automation, Qingdao University, Qingdao 266071, ChinaSchool of Mathematics and Statistics, Qingdao University, Qingdao 266071, ChinaWe consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interval of a fixed duration. Over time, information about the game structure will be updated. The subject of the current paper is to construct players’ cooperative strategies, their cooperative trajectory, the characteristic function, and the cooperative solution for this class of differential games with continuous updating, particularly by using Pontryagin’s maximum principle as the optimality conditions. In order to demonstrate this method’s novelty, we propose to compare cooperative strategies, trajectories, characteristic functions, and corresponding Shapley values for a classic (initial) differential game and a differential game with continuous updating. Our approach provides a means of more profound modeling of conflict controlled processes. In a particular example, we demonstrate that players’ behavior is braver at the beginning of the game with continuous updating because they lack the information for the whole game, and they are “intrinsically time-inconsistent”. In contrast, in the initial model, the players are more cautious, which implies they dare not emit too much pollution at first.https://www.mdpi.com/2227-7390/9/2/163differential games with continuous updatingPontryagin maximum principleopen-loop Nash equilibriumHamiltoniancooperative differential game<i>δ</i>-characteristic function |
| spellingShingle | Jiangjing Zhou Anna Tur Ovanes Petrosian Hongwei Gao Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle Mathematics differential games with continuous updating Pontryagin maximum principle open-loop Nash equilibrium Hamiltonian cooperative differential game <i>δ</i>-characteristic function |
| title | Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle |
| title_full | Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle |
| title_fullStr | Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle |
| title_full_unstemmed | Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle |
| title_short | Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle |
| title_sort | transferable utility cooperative differential games with continuous updating using pontryagin maximum principle |
| topic | differential games with continuous updating Pontryagin maximum principle open-loop Nash equilibrium Hamiltonian cooperative differential game <i>δ</i>-characteristic function |
| url | https://www.mdpi.com/2227-7390/9/2/163 |
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