Side-payment contracts in two-person nonzero-sum supply chain games : review, discussion and applications

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Journal article

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European Journal of Operational Research

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Decision analysis, Game theory, Side-payment contracts, Supply chain coordination, Cournot game, Bertrand game, Substitutable products, Forward buying


This paper investigates supply chain coordination with side-payment contracts. We first summarize specific side-payment contracts and present our review on the literature that developed general side-payment schemes to coordinate supply chains. Following our review, we discuss two criteria that a proper side-payment contract must satisfy, and accordingly introduce a decision-dependent transfer payment function and a constant transfer term. We present the condition that the transfer function must satisfy, and use Nash arbitration scheme and Shapley value to compute the constant transfer term and derive its closed-form solution. Next, we provide a five-step procedure for the development of side-payment contract, and apply it to four supply chain games: Cournot and Bertrand games, a two-retailer supply chain game with substitutable products and a one-supplier, one-retailer supply chain. More specifically, for the Cournot game, we construct a linear transfer function and a constant side-payment to coordinate two producers. For the Bertrand game, we build a nonlinear transfer function which is equivalent to a revenue-sharing contract, and show that the constant term is zero and two firms in the game equally share the system-wide profit. For a supply chain with substitutable products, we present a side-payment contract to coordinate two retailers. For a two-echelon supply chain, we develop a proper side-payment scheme that can coordinate the supply chain and also help reduce the impact of forward buying on supply chain performance.



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Copyright © 2008 Elsevier B.V. All rights reserved.

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Leng, M., & Zhu, A. (2009). Side-payment contracts in two-person nonzero-sum supply chain games: Review, discussion and applications. European Journal of Operational Research, 196(2), 600-618. doi: 10.1016/j.ejor.2008.03.029