A multi-player game equilibrium problem based on stochastic variational inequalities
In this paper, we studied a generalized Nash equilibrium problem where the constraint conditions were limited to a certain probability. The existence of an equilibrium solution for the vector-valued optimization problem was verified using Ky Fan's inequality and Lusin's theorem, considerin...
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AIMS Press
2024-09-01
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| Series: | AIMS Mathematics |
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| author | Cunlin Li Wenyu Zhang Baojun Yang Hooi Min Yee |
| author_facet | Cunlin Li Wenyu Zhang Baojun Yang Hooi Min Yee |
| author_sort | Cunlin Li |
| collection | DOAJ |
| description | In this paper, we studied a generalized Nash equilibrium problem where the constraint conditions were limited to a certain probability. The existence of an equilibrium solution for the vector-valued optimization problem was verified using Ky Fan's inequality and Lusin's theorem, considering the conditions of lower semi-continuity and concavity. Based on the study of the variational inequality method, we proposed a new algorithm to solve the problem. Furthermore, we analyzed the convergence of the algorithm. Finally, we applied the model to examine the economic benefits of digital currency issuance, corroborating the algorithm's effectiveness with a concrete numerical example. |
| format | Article |
| id | doaj-art-18af80ff4ecc4f80897f7fac83a8f57d |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-18af80ff4ecc4f80897f7fac83a8f57d2025-08-20T01:54:38ZengAIMS PressAIMS Mathematics2473-69882024-09-0199260352604810.3934/math.20241271A multi-player game equilibrium problem based on stochastic variational inequalitiesCunlin Li 0Wenyu Zhang1Baojun Yang2Hooi Min Yee 31. Ningxia Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Wenchang Street, Yinchuan, 750021, Ningxia, China2. School of Mathematics and Information Science, North Minzu University, Wenchang Street, Yinchuan, 750021, Ningxia, China3. School of Business, North Minzu University, Wenchang Street, Yinchuan, 750021, Ningxia, China4. Civil Engineering Studies, College of Engineering, Universiti Teknologi MARA, Penang Branch, Permatang Pauh Campus, 13500 Permatang Pauh, Pulau Pinang, MalaysiaIn this paper, we studied a generalized Nash equilibrium problem where the constraint conditions were limited to a certain probability. The existence of an equilibrium solution for the vector-valued optimization problem was verified using Ky Fan's inequality and Lusin's theorem, considering the conditions of lower semi-continuity and concavity. Based on the study of the variational inequality method, we proposed a new algorithm to solve the problem. Furthermore, we analyzed the convergence of the algorithm. Finally, we applied the model to examine the economic benefits of digital currency issuance, corroborating the algorithm's effectiveness with a concrete numerical example.https://aimspress.com/article/doi/10.3934/math.20241271MailInfo.exe -i d:\temp\test -o d:\temp\MailInfo\result4.csv -amulti-player gamenonlinear programmingrandom variational inequality |
| spellingShingle | Cunlin Li Wenyu Zhang Baojun Yang Hooi Min Yee A multi-player game equilibrium problem based on stochastic variational inequalities AIMS Mathematics multi-player game nonlinear programming random variational inequality |
| title | A multi-player game equilibrium problem based on stochastic variational inequalities |
| title_full | A multi-player game equilibrium problem based on stochastic variational inequalities |
| title_fullStr | A multi-player game equilibrium problem based on stochastic variational inequalities |
| title_full_unstemmed | A multi-player game equilibrium problem based on stochastic variational inequalities |
| title_short | A multi-player game equilibrium problem based on stochastic variational inequalities |
| title_sort | multi player game equilibrium problem based on stochastic variational inequalities |
| topic | multi-player game nonlinear programming random variational inequality |
| url | https://aimspress.com/article/doi/10.3934/math.20241271MailInfo.exe -i d:\temp\test -o d:\temp\MailInfo\result4.csv -a |
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