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


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  • Gerichhausen, M.
  • Berkhout, E.D.
  • Hamers, H.J.M.
  • Manyong, V.M.

    (Tilburg University, Center for Economic Research)

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    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.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-62.

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    Date of creation: 2008
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    Handle: RePEc:dgr:kubcen:200862

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    Keywords: Linear Programming; Agriculture; Household models; Cooperative Game Theory; Nigeria;

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    1. de Janvry, Alain & Fafchamps, Marcel & Sadoulet, Elisabeth, 1991. "Peasant Household Behaviour with Missing Markets: Some Paradoxes Explained," Economic Journal, Royal Economic Society, vol. 101(409), pages 1400-417, November.
    2. Ruben, Ruerd & Pender, John, 2004. "Rural diversity and heterogeneity in less-favoured areas: the quest for policy targeting," Food Policy, Elsevier, vol. 29(4), pages 303-320, August.
    3. Mitsuo Suzuki & Mikio Nakayama, 1976. "The Cost Assignment of the Cooperative Water Resource Development: A Game Theoretical Approach," Management Science, INFORMS, vol. 22(10), pages 1081-1086, June.
    4. Aadland, David & Kolpin, Van, 1998. "Shared irrigation costs: An empirical and axiomatic analysis," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 203-218, March.
    5. Andrew Dorward, 2006. "Markets and pro-poor agricultural growth: insights from livelihood and informal rural economy models in Malawi," Agricultural Economics, International Association of Agricultural Economists, vol. 35(2), pages 157-169, 09.
    6. Cruijssen, F.C.A.M. & Borm, P.E.M. & Fleuren, H.A. & Hamers, H.J.M., 2005. "Insinking: A Methodology to Exploit Synergy in Transportation," Discussion Paper 2005-121, Tilburg University, Center for Economic Research.
    7. Abdoulaye, Tahirou & Sanders, John H., 2006. "New technologies, marketing strategies and public policy for traditional food crops: Millet in Niger," Agricultural Systems, Elsevier, vol. 90(1-3), pages 272-292, October.
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