Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10898-012-9894-3
Title: Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management
Authors: Ang, J. 
Fukushima, M.
Meng, F. 
Noda, T.
Sun, J. 
Keywords: Leader-follower game
Nash equilibrium
Nonlinear programming
Supply chain management
Issue Date: Aug-2013
Source: Ang, J., Fukushima, M., Meng, F., Noda, T., Sun, J. (2013-08). Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management. Journal of Global Optimization 56 (4) : 1297-1312. ScholarBank@NUS Repository. https://doi.org/10.1007/s10898-012-9894-3
Abstract: We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier's profit depends not only on its own delivery frequency, but also on other suppliers' frequencies through their impact on manufacturer's purchase allocation to the suppliers. We first solve the follower's (manufacturer's) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders' (suppliers') game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved. © 2012 Springer Science+Business Media, LLC.
Source Title: Journal of Global Optimization
URI: http://scholarbank.nus.edu.sg/handle/10635/116721
ISSN: 09255001
DOI: 10.1007/s10898-012-9894-3
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