Side-payment contracts in two-person nonzero-sum supply chain games : review, discussion and applications
Document Type
Journal article
Source Publication
European Journal of Operational Research
Publication Date
7-16-2009
Volume
196
Issue
2
First Page
600
Last Page
618
Publisher
Elsevier BV
Keywords
Decision analysis, Game theory, Side-payment contracts, Supply chain coordination, Cournot game, Bertrand game, Substitutable products, Forward buying
Abstract
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.
DOI
10.1016/j.ejor.2008.03.029
Print ISSN
03772217
E-ISSN
18726860
Funding Information
This research was financially supported by the Research and Postgraduate Studies Committee of Lingnan University under Research Project No. DR07B8.
Publisher Statement
Copyright © 2008 Elsevier B.V. All rights reserved.
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Full-text Version
Publisher’s Version
Language
English
Recommended Citation
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