This study investigates whether a group of independent agricultural producers willingly forms a coalition to jointly cope with yield uncertainty in contract farming. The agricultural producers’ cooperative game problem in contract farming is formulated as a two‐stage stochastic linear program. Using the strong duality theory of stochastic linear programs, we not only prove that the core of agricultural producers’ cooperative game is nonempty but also provide a simple way to compute a profit allocation policy in the core. We establish the convexity of agricultural producers’ cooperative game so that the game has population monotonicity, which gives agricultural producers an incentive to expand their current coalition. We then analyze the agricultural producers’ cooperative game with a concave cost structure, which may exhibit economies of scale for production. Taking advantage of the proposed stochastic duality approach, the agricultural producers’ cooperative game with a concave cost structure is also shown to have a nonempty core.

中文翻译：

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产量不确定性下的合同农业问题和博弈

这项研究调查了一群独立的农业生产者是否愿意组建一个联盟，共同应对合同农业中的产量不确定性。合同农业中的农业生产者合作博弈问题被表述为两阶段随机线性程序。利用随机线性规划的强对偶理论，我们不仅证明了农业生产者合作博弈的核心是非空的，而且提供了一种计算核心利润分配策略的简单方法。我们建立了农业生产者合作博弈的凸性，以使该博弈具有人口单调性，这给农业生产者提供了扩大其现有联盟的动力。然后，我们分析了具有凹成本结构的农业生产者的合作博弈，这可能会显示出规模生产的经济效益。利用提出的随机对偶方法，具有凹成本结构的农业生产者合作博弈也被证明具有非空核心。