Contract farming problems and games under yield uncertainty

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.