Análise matemática aplicada à teoria de jogos

Abstract

This work presents applications of mathematical analysis in game theory. Initially we present an introduction to economical game theory, exploring the concept of normal-form game. We consider some concepts of game solution, including Nash Equilibrium, and we introduce the concept of mixed strategies and best response functions. Based on the relationship between Nash equilibria and fixed points of the best response function of the game, we prove the theorem of existence of Nash equilibrium, using Kakutani’s Fixed Point Theorem. We study two specific kind of games: 2x2 games and symmetric games. Finally, we present an introduction to evolutionary game theory exploring the concept of evolutionary stable strategy, and we prove two characterizations of this concept: uniform invasion barrier and local superiority.