Iran is the major producer of pistachio nuts in the world. Iran dominated the international pistachio export markets until 1982, when a new competitor, the United States, emerged in the international markets. Currently, both Iran and the U.S. are major pistachio exporters to Japan. The empirical question being investigated in this study is whether the Japanese pistachio import market is best characterized by Cournot or Bertrand duopoly competition or some other form of game. In this research, using historical data on pistachio prices and quantity imported by Japan from Iran and the U.S., demand functions for these two main exporters are estimated. Considering two different strategic variables, quantity and price, full information maximum likelihood (FIML) resulted in different estimates. Normalized likelihood ratio statistics is used for the model comparison. Having proper game-specific nonlinear-equation restrictions enabled us to form six alternative models. The model that best fit the data was the Stackelberg model with US quantity leadership.