Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference
To prove the existence of Nash equilibrium by traditional ways, a common condition that the preference of players must be complete has to be considered. This paper presents a new method to improve it. Based on the incomplete preference corresponding to equivalence class set being a partial order set...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/3737253 |
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| _version_ | 1849305453329121280 |
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| author | Xingchang Li |
| author_facet | Xingchang Li |
| author_sort | Xingchang Li |
| collection | DOAJ |
| description | To prove the existence of Nash equilibrium by traditional ways, a common condition that the preference of players must be complete has to be considered. This paper presents a new method to improve it. Based on the incomplete preference corresponding to equivalence class set being a partial order set, we translate the incomplete preference problems into the partial order problems. Using the famous Zorn lemma, we get the existence theorems of fixed point for noncontinuous operators in incomplete preference sets. These new fixed point theorems provide a new way to break through the limitation. Finally, the existence of generalized Nash equilibrium is strictly proved in the n-person noncooperative games under incomplete preference. |
| format | Article |
| id | doaj-art-0a0091e31892447db2cc6ffb28778908 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-0a0091e31892447db2cc6ffb287789082025-08-20T03:55:27ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/37372533737253Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete PreferenceXingchang Li0School of Mathematics and Statistics, Changshu Institute of Technology, Suzhou 215500, ChinaTo prove the existence of Nash equilibrium by traditional ways, a common condition that the preference of players must be complete has to be considered. This paper presents a new method to improve it. Based on the incomplete preference corresponding to equivalence class set being a partial order set, we translate the incomplete preference problems into the partial order problems. Using the famous Zorn lemma, we get the existence theorems of fixed point for noncontinuous operators in incomplete preference sets. These new fixed point theorems provide a new way to break through the limitation. Finally, the existence of generalized Nash equilibrium is strictly proved in the n-person noncooperative games under incomplete preference.http://dx.doi.org/10.1155/2018/3737253 |
| spellingShingle | Xingchang Li Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference Journal of Function Spaces |
| title | Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference |
| title_full | Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference |
| title_fullStr | Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference |
| title_full_unstemmed | Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference |
| title_short | Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference |
| title_sort | existence of generalized nash equilibrium in n person noncooperative games under incomplete preference |
| url | http://dx.doi.org/10.1155/2018/3737253 |
| work_keys_str_mv | AT xingchangli existenceofgeneralizednashequilibriuminnpersonnoncooperativegamesunderincompletepreference |