  In this paper, we focus on decentralized agricultural supply chains
consisting of multiple non-competing distributors satisfying the demand of
their respective markets. These distributors source a single product from a
farmer through an agricultural cooperative, operating in a single period. The
agents have the ability to coordinate their actions to maximize their profits,
and we use cooperative game theory to analyze cooperation among them. The
distributors can engage in joint ordering, increasing their order size, which
leads to a decrease in the price per kilogram. Additionally, distributors have
the opportunity to cooperate with the farmer, securing a reduced price per
kilogram at the cost price, while compensating the farmer for any kilograms not
acquired in the cooperation agreement. We introduce multidistributor-farmer
games and we prove that all the agents have incentives to cooperate. We
demonstrate the existence of stable allocations, where no subgroup of agents
can be better off by separating. Moreover, we propose and characterize a
distribution of the total profit that justly compensates the contribution of
the farmer in any group of distributors. Finally, we explore the conditions
under which the farmer can be compensated in order to maximize their revenues
when cooperating with all players.
