A stackelberg model for decision making in a farming community

In agriculture, farmers have the option of growing different crops based on prices set by a wholesaler. In turn, a wholesaler will set prices based on demand and supply of the different types of produce. Both the wholesaler and the farmers try to make their decision to maximize their profit. In this manuscript, we formulate the decision making as a Stackelberg competition. Such a competition is a two-stage model from game-theory with a leader (wholesalers) and multiple followers (farmers). The leader moves first and make the decision of setting prices. Next, the followers move and decide on their what types of crops to grow by holding competition between them. This cycle continues for multiple seasons. For the model, we use data from a farmingcommunity in North India for behavior of the farmers and data from the Ministry of the Agricultural and Welfare, Govt of India, for the behavior of the wholesalers. We then calculate the generalized Nash equilibrium by a backward induction method. This equilibrium tells us in what fractions crops will be produced in the long run.