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.

翻译：本文聚焦于分散型农业供应链，该供应链由多个非竞争性分销商组成，满足各自市场的需求。这些分销商通过农业合作社从单一农户处采购单一产品，且运营周期为单周期。各主体能够协调行动以最大化利润，我们运用合作博弈理论分析主体间的合作行为。分销商可通过联合订购增加订单规模，从而降低每公斤价格。此外，分销商有机会与农户合作，以成本价获得每公斤产品的优惠价格，同时补偿农户在合作协议中未收购的公斤数。我们引入多分销商-农户博弈模型，并证明所有主体均存在合作动机。我们证明了稳定分配的存在性，即任何子群主体都无法通过分离获得更优收益。进一步，我们提出并刻画了一种总利润分配方案，该方案能公平补偿农户在任何分销商群体中的贡献。最后，我们探索了当农户与所有参与者合作时，为最大化其收益所需的补偿条件。