Cooperative game analysis of a supply chain with one risk-neutral supplier and two risk-averse retailers

Changwen Li, Yongwu Zhou, Yong Lu, Jinsen Guo


Purpose: This paper considers a two-echelon supply chain composed of one risk-neutral supplier and two risk-averse retailers. The retailers obtain production from the supplier and sell them to the market. Based on the cooperative game theory, the paper studies the appropriate profit allocation of the supply chain when all the players cooperate with each other, where the two retailers face a price-sensitive stochastic demand. The two retailers can either determine their retail prices independently, or decide whether or not to cooperate with each other.

Design/methodology/approach: To allocate the system-wide profit among upstream risk-neutral suppliers and two risk-averse downstream retailers, this paper constructed a cooperative game model, considered as the supermodularity of the characteristic function and the Shapley value of the game.

Findings and Originality/value: By analyzing the construction’s cooperative game model, the results show that the profit of the whole supply chain is the highest in the grand coalition structure. This paper also shows that the core of our cooperative game is nonempty, and has the supermodularity property. Based on this, we have computed the Shapley value-based profit allocation for the whole supply chain in a fair manner.

Originality/value: Although there are a lot of literature examined risk aversion in a supply chain, but they did not consider using cooperative game to study this problem. This the first study is in the context of a supply chain with risk aversion problem.


supply chain; risk-averse ;cooperative game; supermodular; Shapley value

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Licencia de Creative Commons 

This work is licensed under a Creative Commons Attribution 4.0 International License

Journal of Industrial Engineering and Management, 2008-2024

Online ISSN: 2013-0953; Print ISSN: 2013-8423; Online DL: B-28744-2008

Publisher: OmniaScience