A Game Theoretic Approach to Analyse Cooperation between Rural Households in Northern Nigeria

Much research focuses on development of new agricultural technologies to reduce poverty levels of the large population of smallholder farms in Sub Saharan Africa. In this paper we argue that smallholders can also increase their production in a different way, namely by using their resources more efficiently through cooperation. This is obtained by grouping their (heterogeneous) resources and making joint decisions based on the aggregate resources. Afterwards, the gains of the joint production are divided, such that each farmer remains independent. This type of cooperation is modeled using linear programming and cooperative game theory. While linear programming establishes insight in optimal farm plans for farmers that cooperate, game theory is used to generate fair divisions of the extra gain that is established by cooperation. The model is applied to a village in Northern Nigeria. Households are clustered based on socio-economic parameters, and we explore cooperation. The optimal farm plan of the cooperative (i.e., farmers cooperate) contains more crops with high market and nutritional value, such as cowpea and sugarcane. We show that the gross margin of the cooperative is 12% higher than the sum of the individual gross margins. To divide these gains, we consider four established solution concepts from game theory that divide these extra gains: the Owen value, Shapley value, compromise value and nucleolus. An interesting result is that all farmers gain from cooperation and that the four solution concepts give similar results. Finally, we show how the provision of micro-credit can be used to stimulate cooperation in practice, benefiting the least-endowed farmers as well.