The aim of this work is to analyze and reflex about the reputation model in the finitely repeated Prisioners’ Dilemma and its applicability in the dupoly’s market. This work, also considerers the conditions under which each player, in the Cournot Duopoly, have the optimal strategy for cooperation in each stage of the game finitely repeated. Results point out that in spite of its limitations, the cooperation can arise and holding up as a result of three basic conditions: payoffs, strategies and the probability of being rational. We think that diverse modifications can be aggregated at this structure for do it more handy.