A Look on Mathematical Fundamentals for Minimax Theorem and Nash Equilibrium Existence

EasyChair Preprint 8049

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.

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

@booklet{EasyChair:8049,
  author    = {Manuel Ferreira},
  title     = {A Look on Mathematical Fundamentals for Minimax Theorem and Nash Equilibrium Existence},
  howpublished = {EasyChair Preprint 8049},
  year      = {EasyChair, 2022}}