# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020172
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## Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution

 1 School of Business Administration, Hunan University, Changsha, 410082, China 2 Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China 3 No.1 Middle School Attached to Central China Normal University, Wuhan, 430223, China

* Corresponding author: Feimin Zhong

Received  November 2019 Revised  October 2020 Early access December 2020

This paper studies a multi-echelon serial supply chain with negotiations over wholesale prices between successive echelons. Two types of bargaining systems with power structures are compared: one adopts the generalized Kalai-Smorodinsky (KS) solution and the other adopts the generalized Nash solution. Our analyses show that, for any KS bargaining system with a given bargaining power structure, there is a Nash bargaining system with another bargaining power structure, such that the two systems are the same. However under the same power structure, the generalized KS solution results in lower wholesale price and higher total supply chain profit than the Nash solution does. Finally, we characterize the necessary and sufficient condition of the bargaining power structure under which the KS bargaining system Pareto dominates the Nash bargaining system, and the set characterized by such condition does not shrink to an empty set as the number of echelons increases to infinity.

Citation: Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020172
##### References:

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##### References:
Generalized KS solution for two players
The multi-echelon supply chain
$n = 3$ and $d = 1$
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