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A LOOK ON MATHEMATICAL FUNDAMENTALS FOR MINIMAX THEOREM AND NASH EQUILIBRIUM EXISTENCE
Event Title
19th Conference on Applied Mathematics APLIMAT 2020
Year (definitive publication)
2020
Language
English
Country
Slovakia
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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 plays 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 ISCTE-Instituto Universitário de Lisboa and ISTAR-IUL for their support.
Keywords
minimax theorem,Nash equilibrium,Kakutani theorem
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
- Economics and Business - Social Sciences
Funding Records
| Funding Reference | Funding Entity |
|---|---|
| UID/MULTI/04466/ 2019 | FCT - Fundação para a Ciência e Tecnologia, I.P. |
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