Existence of Generalized Nash Equilibrium in n-Person Noncooperative Games under Incomplete Preference. (9th October 2018)

• Record Type: Journal Article
• Authors: Li, Xingchang
• Other Names: Zhang Xinguang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2018(2018)
• Publication Date: 2018-10-09
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2018/3737253
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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 then - person noncooperative games under incomplete preference.