Order-clustered fixed point theorems on chain-complete preordered sets and their applications to extended and generalized Nash equilibria

Fixexd point theory and applications

Linsen Xie¹  Jinlu Li²  Wenshan Yang³ 

[1] Department of Mathematics, Lishui University, Lishui, China;Department of Mathematics, Shawnee State University, Portsmouth, USA;Department of Mathematics, Zhejiang Normal University, Jinhua, China

关键词: chain-complete preordered sets;    order-clustered fixed point;    Abian-Brown fixed point theorem;    order-increasing upward mapping;    nonmonetized noncooperative game;    generalized Nash equilibrium;    extended Nash equilibrium;   

DOI  :  10.1186/1687-1812-2013-192

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce the concept of order-clustered fixed point of set-valued mappings on preordered sets and give several generalizations of the extension of the Abian-Brown fixed point theorem provided in (Mas-Colell et al. in Microeconomic Theory, 1995), which is from chain-complete posets to chain-complete preordered sets. By using these generalizations and by applying the order-increasing upward property of set-valued mappings, we prove several existence theorems of the extended and generalized Nash equilibria of nonmonetized noncooperative games on chain-complete preordered sets. MSC:46B42, 47H10, 58J20, 91A06, 91A10.

【 授权许可】

CC BY