In this paper a game theoretic model will be developed for the determination of acreage allocation among four crops--wheat, corn, oats, and soybeans. The model will be functionally dependent upon statistical demand elasticity curves and will be applied to data for the period 1948-1958 for the United States. Elements of an individual farmer's strategy will be presented. In addition, the optimal game theoretic acreage allocation for the above period for total United States production will be compared with the actual acreage allocation for the four crops. The discussion throws light on the reasons for some of the variations in annual acreage for the above crops.