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Game Theoretic Analysis of a Distribution System with Customer Market Search

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  • Yue Dai
  • Xiuli Chao
  • Shu-Cherng Fang
  • Henry Nuttle

Abstract

Consider a distribution system with one supplier and two retailers. When a stockout occurs at one retailer customers may go to the other retailer. We study a single period model in which the supplier may have infinite or finite capacity. In the latter case, if the total quantity ordered (claimed) by the retailers exceeds the supplier’s capacity, an allocation policy is involved to assign the limited capacity to the retailers. We analyze the inventory control decisions for the retailers using a game theoretical approach. The necessary and sufficient conditions are derived for the existence of a unique Nash equilibrium. A computational procedure is also proposed to calculate the Nash equilibrium. In case the Nash equilibrium does not exist, we use the concept of Stackelberg game to develop optimal strategies for both the leader and the follower. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Yue Dai & Xiuli Chao & Shu-Cherng Fang & Henry Nuttle, 2005. "Game Theoretic Analysis of a Distribution System with Customer Market Search," Annals of Operations Research, Springer, vol. 135(1), pages 223-228, March.
    • Handle: RePEc:spr:annopr:v:135:y:2005:i:1:p:223-228:10.1007/s10479-005-6243-7
    DOI: 10.1007/s10479-005-6243-7
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    References listed on IDEAS

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    1. Barry A. Pasternack & Zvi Drezner, 1991. "Optimal inventory policies for substitutable commodities with stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 221-240, April.
    2. Ravi Anupindi & Yehuda Bassok, 1999. "Centralization of Stocks: Retailers vs. Manufacturer," Management Science, INFORMS, vol. 45(2), pages 178-191, February.
    3. Mahmut Parlar, 1988. "Game theoretic analysis of the substitutable product inventory problem with random demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 397-409, June.
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    Citations

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    Cited by:

    1. Yue Dai & Shu-Cherng Fang & Xiaoli Ling & Henry Nuttle, 2008. "Risk pooling strategy in a multi-echelon supply chain with price-sensitive demand," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 391-421, June.
    2. Amir Gandomi & Amirhossein Bazargan & Saeed Zolfaghari, 2019. "Designing competitive loyalty programs: a stochastic game-theoretic model to guide the choice of reward structure," Annals of Operations Research, Springer, vol. 280(1), pages 267-298, September.
    3. Masih Fadaki & Babak Abbasi & Prem Chhetri, 2022. "Quantum game approach for capacity allocation decisions under strategic reasoning," Computational Management Science, Springer, vol. 19(3), pages 491-512, July.
    4. İsmail Bakal & Nesim Erkip & Refik Güllü, 2011. "Value of supplier’s capacity information in a two-echelon supply chain," Annals of Operations Research, Springer, vol. 191(1), pages 115-135, November.
    5. Qi, Yuqing & Ni, Weihong & Shi, Kuiran, 2015. "Game theoretic analysis of one manufacturer two retailer supply chain with customer market search," International Journal of Production Economics, Elsevier, vol. 164(C), pages 57-64.
    6. Yue Dai & Xiuli Chao & Shu‐Cherng Fang & Henry L.W. Nuttle, 2006. "Capacity allocation with traditional and Internet channels," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 772-787, December.

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