Contracting Mechanisms for Stable Sourcing Networks

Problem definition: We study profit allocation for a sourcing network, in which a buyer sources from a set of differentiated suppliers with limited capacity under uncertain demand for the final product. Whereas the buyer takes the lead in forming the sourcing network and designing the contract mechanism, due to their substantial bargaining power, the suppliers take the lead in determining the terms of the contract. Academic/practical relevance: We identify contracting mechanisms that will ensure the stability of the sourcing network in the long term, where a stable sourcing network requires an effective profit-allocation scheme that motivates all members to join and stay in the network. Methodology: We apply methods from game theory to model the network and analyze the Nash equilibrium of a noncooperative game under a proposed contracting mechanism. We then use a cooperative game model to study the stability of the resulting equilibrium. Results: We show that the optimal network profit, as a set function of the set of suppliers, is submodular, which allows us to demonstrate that the core of the cooperative game is not empty. We also establish a set of conditions that are equivalent to, but much simpler than, the original conditions for the core. We use these results to demonstrate that the proposed fixed-fee contracting mechanism can implement a stable network in the competitive setting by achieving a profit allocation that is in the core of the cooperative game. We also demonstrate that the grand coalition is stable in a farsighted sense under the Shapley value allocation. Managerial implications: Under the fixed-fee mechanism, the buyer’s decisions maximize the network profit, and each supplier earns a profit equal to its marginal contribution. When the aggregate capacity of the supplier network is high relative to demand, or demand is more likely to be small, the fixed-fee mechanism is likely to outperform the Shapley value allocation from the perspective of the buyer.

Duke Scholars

Author Jing-Sheng Song Fuqua School of Business