This paper attempts to study the collaboration between fiscal and monetary policy in a game-theoretic approach. The significant nature of coordination between these two policymakers is essential to the growth of any economic, holding to the facts that certain decisions taken by one institution may have devastating effects on the other institution, by resulting in loss of social welfare of the citizens of that nation. In this logic, this paper derived optimal monetary and fiscal policies in one context of coordination or form of interaction using the Two-stage game with complete and perfect information in normal-form representation of the prisoners dilemma: when the two institutions minimize their losses by only taking into account their objectives or responsibilities they owed to the society, formulation of solution known as the Nash equilibrium solution; when an institution moves first in pursuance of the objectives in improving the social welfare and the other follows, in a mechanism known as the optimal solution; when institutions behave cooperatively, seeking common goals. Like in the case Brazilian economy, the two institutions simultaneously demonstrated coordination at the level were both the monetary and fiscal authorities choose the (4, 4) as the optimal point in stabilizing inflation and output remains at its maximum level, that a minimal loss is found when there is a Nash equilibrium, particularly when monetary policy is the leader of the economy and fiscal policy follows.