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An approximation theorem and generic convergence for equilibrium problems.
Xiaoling Qiu1, Wensheng Jia1,2, Dingtao Peng1
11School of Mathematics and Statistic, Guizhou University, Guiyang, China.
Journal of Inequalities and Applications
|February 16, 2018
Summary
This study introduces an approximation theorem for equilibrium problems, demonstrating how bounded rationality approaches full rationality. It also proves generic uniqueness and convergence for monotone equilibrium problems using set-valued analysis.
Area of Science:
- Mathematical Economics
- Optimization Theory
- Game Theory
Background:
- Equilibrium problems are fundamental in various fields, but their solutions can be complex.
- Bounded rationality offers a more realistic model of decision-making than perfect rationality.
- Existing algorithms for equilibrium problems often lack theoretical guarantees.
Purpose of the Study:
- To establish an approximation theorem for equilibrium problems.
- To provide theoretical foundations for computational algorithms.
- To analyze the properties of solutions for monotone equilibrium problems.
Main Methods:
- Development of an approximation theorem.
- Application of set-valued analysis techniques.
- Investigation using Baire category theory.
Main Results:
- An approximation theorem illustrating bounded rationality's convergence to full rationality.
- Generic uniqueness and convergence of solutions for monotone equilibrium problems.
- Theoretical support for a range of algorithms.
Conclusions:
- The findings offer significant theoretical backing for equilibrium problem algorithms.
- Set-valued analysis provides powerful tools for understanding solution properties.
- The study bridges bounded rationality concepts with mathematical equilibrium theory.
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