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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Main Author: Xingchang Li
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2018/3737253
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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.
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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