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Establishing Nash equilibrium of the manufacturer–supplier game in supply chain management

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  • James Ang
  • Masao Fukushima
  • Fanwen Meng
  • Takahiro Noda
  • Jie Sun

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. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • James Ang & Masao Fukushima & Fanwen Meng & Takahiro Noda & Jie Sun, 2013. "Establishing Nash equilibrium of the manufacturer–supplier game in supply chain management," Journal of Global Optimization, Springer, vol. 56(4), pages 1297-1312, August.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1297-1312
    DOI: 10.1007/s10898-012-9894-3
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    References listed on IDEAS

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    Cited by:

    1. Anna Nagurney & Min Yu & Deniz Besik, 2017. "Supply chain network capacity competition with outsourcing: a variational equilibrium framework," Journal of Global Optimization, Springer, vol. 69(1), pages 231-254, September.

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