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Publication Detailed Description
A Look on Mathematical Fundamentals for Minimax Theorem and Nash Equilibrium Existence
Document Title
EasyChair Preprint Nº 8049
Year (definitive publication)
2022
Language
English
Country
United Kingdom
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Abstract
We present two results of Game Theory, very important in Economics: minimax theorem and Nash equilibrium existence, together with their mathematical fundamentals. For minimax theorem, the mathematical structure considered is real Hilbert Spaces. Moreover, the convex sets strict separation play here an important role. For Nash equilibrium existence, Kakutani’s theorem is the key result to consider. Then follows a presentation of some propositions that identify matches between those outcomes.
Acknowledgements
This work is financed by national funds through FCT - Fundação para a Ciência e
Tecnologia, I.P., under the project UID/Multi/04466/2019. Furthermore, I would like to
thank the Instituto Universitário de Lisboa and ISTAR-IUL for their support.
Keywords
convex sets strict separation,Kakutani’s theorem,minimax theorem,Nash equilibrium
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
- Computer and Information Sciences - Natural Sciences
Funding Records
| Funding Reference | Funding Entity |
|---|---|
| UID/Multi/04466/2019 | FCT-Fundação para a Ciência e Tecnologia, I.P. |
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