On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory
In this paper, first a brief history of equilibrium problems(EP) and generalized implicit vector equilibrium problems(GIVEP) are given. Then some existence theorems for GIVEP are presented, also some suitable conditions in order the solution set of GIVEP is compact and convex for set-valued mappings...
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| Format: | Article |
| Language: | English |
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Islamic Azad University of Arak
2022-04-01
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| Series: | Advances in Mathematical Finance and Applications |
| Subjects: | |
| Online Access: | https://amfa.arak.iau.ir/article_686428_2f6c35e8feb00f3a874a6915a89f3d35.pdf |
| _version_ | 1811245858717433856 |
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| author | Parastoo Zangenehmehr Ali Farajzadeh |
| author_facet | Parastoo Zangenehmehr Ali Farajzadeh |
| author_sort | Parastoo Zangenehmehr |
| collection | DOAJ |
| description | In this paper, first a brief history of equilibrium problems(EP) and generalized implicit vector equilibrium problems(GIVEP) are given. Then some existence theorems for GIVEP are presented, also some suitable conditions in order the solution set of GIVEP is compact and convex for set-valued mappings whose are a subset of the cartesian product of Hausdorff topological vector space and their range is a subset of a topological space values (not necessarily locally convex or a topological vector space). In almost all of published results for GIVEP the set-valued mappings are considered from a topological vector space(locally convex topological vector space) to a topological vector space while in this paper the range of the set-valued mappings are a subsets of a topological spaces. As applications of our results, we derive some suitable conditions for existing a normalized Nash equilibrium problems when the number of players are finite and the abstract case, that is infinite players. Finally, a numerical result, as an application of the main results, is given. The method used for proving the existence theorems is based on finite intersection theorems and Ky-Fan’s theorem. The results of this paper, can be considered as suitable generalizations of the published paper in this area. |
| first_indexed | 2024-04-12T14:45:38Z |
| format | Article |
| id | doaj.art-d7891f05116045aa84ec8337cf910da5 |
| institution | Directory Open Access Journal |
| issn | 2538-5569 2645-4610 |
| language | English |
| last_indexed | 2024-04-12T14:45:38Z |
| publishDate | 2022-04-01 |
| publisher | Islamic Azad University of Arak |
| record_format | Article |
| series | Advances in Mathematical Finance and Applications |
| spelling | doaj.art-d7891f05116045aa84ec8337cf910da52022-12-22T03:28:40ZengIslamic Azad University of ArakAdvances in Mathematical Finance and Applications2538-55692645-46102022-04-017239140410.22034/amfa.2021.1935453.1617686428On Solutions of Generalized Implicit Equilibrium Problems with Application in Game TheoryParastoo Zangenehmehr0Ali Farajzadeh1Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, IranDepartment of Mathematics, Razi University, Kermanshah, 67149, Iran.In this paper, first a brief history of equilibrium problems(EP) and generalized implicit vector equilibrium problems(GIVEP) are given. Then some existence theorems for GIVEP are presented, also some suitable conditions in order the solution set of GIVEP is compact and convex for set-valued mappings whose are a subset of the cartesian product of Hausdorff topological vector space and their range is a subset of a topological space values (not necessarily locally convex or a topological vector space). In almost all of published results for GIVEP the set-valued mappings are considered from a topological vector space(locally convex topological vector space) to a topological vector space while in this paper the range of the set-valued mappings are a subsets of a topological spaces. As applications of our results, we derive some suitable conditions for existing a normalized Nash equilibrium problems when the number of players are finite and the abstract case, that is infinite players. Finally, a numerical result, as an application of the main results, is given. The method used for proving the existence theorems is based on finite intersection theorems and Ky-Fan’s theorem. The results of this paper, can be considered as suitable generalizations of the published paper in this area.https://amfa.arak.iau.ir/article_686428_2f6c35e8feb00f3a874a6915a89f3d35.pdfkkm mappingset-valued mappingfinite intersection propertyupper semicontinuous mappinggeneralized nash equilibrium problem |
| spellingShingle | Parastoo Zangenehmehr Ali Farajzadeh On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory Advances in Mathematical Finance and Applications kkm mapping set-valued mapping finite intersection property upper semicontinuous mapping generalized nash equilibrium problem |
| title | On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory |
| title_full | On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory |
| title_fullStr | On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory |
| title_full_unstemmed | On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory |
| title_short | On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory |
| title_sort | on solutions of generalized implicit equilibrium problems with application in game theory |
| topic | kkm mapping set-valued mapping finite intersection property upper semicontinuous mapping generalized nash equilibrium problem |
| url | https://amfa.arak.iau.ir/article_686428_2f6c35e8feb00f3a874a6915a89f3d35.pdf |
| work_keys_str_mv | AT parastoozangenehmehr onsolutionsofgeneralizedimplicitequilibriumproblemswithapplicationingametheory AT alifarajzadeh onsolutionsofgeneralizedimplicitequilibriumproblemswithapplicationingametheory |