This study objective at investigating the Brazilian soybean complex in the period 1990 to 2006, using the theoretical model of Brander-Spencer (1984) and the instrument of strategies based on game theory. The methodology used to estimate the payoffs of the game between Brazil and the United States was the model of vector autoregression (VAR). The analysis of oligopoly, this paper will be based on the Cournot model. For the Cournot model firms produce homogeneous goods and each one considers a fixed level of production of its competitor. It was possible to measure and analyze, through non-cooperative games, the strategic decisions of Brazil to the choices facing the United States, highlighting the reaction function for the sector on soya. The results indicate a dominant strategy in the Brazilian case, it appears that the best strategy for Brazil's high production. Since, in case the U.S. does not subsidize their producers, the estimates showed that the rate of growth of Brazilian exports is positive and represents the best choice, independent of the choice of the United States.