Nonexpansive Mappings in Fixed-Point Iterations and Their Applications in Game Theory
Article ID: 10159
Vol 7, Issue 10, 2024
Vol 7, Issue 10, 2024
Abstract
This paper explores the theoretical foundation of non-expansive mappings in fixed-point iteration and its specific applications in
game theory. As a mapping that maintains or reduces the distance between elements, non-expansive mappings provide an effective mathematical tool for finding stable strategies in dynamic games through their inherent convergence properties. The article first introduces the basic
concepts of fixed-point theory and defines non-expansive mappings, then analyzes their application in solving Nash equilibria in game theory, with a particular emphasis on the stability and efficiency of iterative methods in the solution process. Additionally, through mathematical
modeling and case analysis, this study demonstrates the practical effects and potential applications of non-expansive mappings in multi-stage
games and complex strategy updates. This research not only enhances the understanding of fixed-point iteration methods in both theory and
practice but also offers new perspectives and methods for addressing high-dimensional strategy spaces in game theory.
game theory. As a mapping that maintains or reduces the distance between elements, non-expansive mappings provide an effective mathematical tool for finding stable strategies in dynamic games through their inherent convergence properties. The article first introduces the basic
concepts of fixed-point theory and defines non-expansive mappings, then analyzes their application in solving Nash equilibria in game theory, with a particular emphasis on the stability and efficiency of iterative methods in the solution process. Additionally, through mathematical
modeling and case analysis, this study demonstrates the practical effects and potential applications of non-expansive mappings in multi-stage
games and complex strategy updates. This research not only enhances the understanding of fixed-point iteration methods in both theory and
practice but also offers new perspectives and methods for addressing high-dimensional strategy spaces in game theory.
Keywords
Fixed-Point Iteration; Non-Expansive Mapping; Game Theory
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DOI: https://doi.org/10.18686/ijmss.v7i10.10159
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