Maximal element theorems in product FC-spaces and generalized games

By Xie Ping Ding. 2005

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Let I be a finite or infinite index set, X be a topological space and (Yi,{φNi})i∈I be a family of finitely continuous topological spaces (in short, FC-space). For each i∈I, let Ai:X→2Yi be a set-valued mapping. Some existence theorems of maximal elements for the family {Ai}i∈I are established under noncompact setting of FC-spaces. As applications, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in noncompact FC-spaces. These theorems improve, unify and generalize many important results in recent literature.

Subfields: Computational Theory and Mathematics, Economics and Econometrics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/089b7842c584bba793562f89b2d790df6203faa6