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.

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.

convex sets strict separation,Kakutani’s theorem,minimax theorem,Nash equilibrium

• Matemáticas - Ciências Naturais
• Ciências da Computação e da Informação - Ciências Naturais