In this thesis some details of mathematical models related to or describing the behavior of producers at not totally competitive markets are elaborated. The focus is on presenting how the developments in Game Theory made it possible to consider it as a conjoint framework of all formerly introduced Oligopoly Market models in Mathematical Economy. In particular, we present the concepts of strategic games and Nash Equilibrium. We determine the best response mappings and the equilibrium in Cournot's and Bertrand's Duopoly Markets with linear demand. Oligopoly Markets are investigated as well.