In the paper, a simplified mathematical economic model of a localized grain market is investigated. Model assumptions are the following: the market structure is a monopsony, spatial distribution of market participants and transportation and marketing costs are not considered, the market is a single-product market, there is no grain resale among manufacturers. Grain market participants are grain manufacturers and grain processing companies. The grain processing companies dominate the market and set a grain purchasing price. The grain manufacturers determine the supply quantity to satisfy the needs of the grain processing companies. The simulated system is presented in a game-theoretic and aggregate form. The paper demonstrates and investigates features of three types of solutions: a G1 strategies solution, a Nash’s equilibrium solution, and guaranteed results under the assumption that the market is in equilibrium state. It is proved that the solution for this model is a Nash’s equilibrium solution under a certain conditions applied to the cost function of grain manufacturers.