Abstract
In this paper, we examine some properties of chain-complete posets and introduce the concept of universally inductive posets. By applying these properties, we provide several extensions of Abian-Brown fixed point theorem from single-valued mappings to set-valued mappings on chain-complete posets and on compact subsets of partially ordered topological spaces. As applications of these fixed point theorems, we explore the existence of generalized Nash equilibrium for strategic games with partially ordered preferences. MSC:06F30, 91A06, 91A18.
Highlights
In game theory, the players usually have normal preferences on the outcomes of the games
In this paper, we develop more fixed point theorems in posets with set-valued mappings, which is applied to solving the Nash equilibrium problems for strategic games with partially ordered preferences
3 Several fixed point theorems on partially ordered topological spaces Let (X, X) and (U, U ) be posets and let F : X → U \{∅} be a set-valued mapping
Summary
The players (or the decision makers) usually have normal preferences (i.e. completely ordered preferences) on the outcomes of the games. We give some examples of partially ordered topological vector spaces and chain complete subsets. 3 Several fixed point theorems on partially ordered topological spaces Let (X, X) and (U, U ) be posets and let F : X → U \{∅} be a set-valued mapping.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call