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Game theoretic analysis of maximum cooperative purchasing situations

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  • Mirjam Groote Schaarsberg
  • Peter Borm
  • Herbert Hamers
  • Hans Reijnierse

Abstract

This article introduces maximum cooperative purchasing (MCP)‐situations, a new class of cooperative purchasing situations. Next, an explicit alternative mathematical characterization of the nucleolus of cooperative games is provided. The allocation of possible cost savings in MCP‐situations, in which the unit price depends on the largest order quantity within a group of players, is analyzed by defining corresponding cooperative MCP‐games. We show that a decreasing unit price is a sufficient condition for a nonempty core: there is a set of marginal vectors that belong to the core. The nucleolus of an MCP‐game can be derived in polynomial time from one of these marginal vectors. To show this result, we use the new mathematical characterization for the nucleolus for cooperative games. Using the decomposition of an MCP‐game into unanimity games, we find an explicit expression for the Shapley value. Finally, the behavior of the solution concepts is compared numerically. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 607–624, 2013

Suggested Citation

  • Mirjam Groote Schaarsberg & Peter Borm & Herbert Hamers & Hans Reijnierse, 2013. "Game theoretic analysis of maximum cooperative purchasing situations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 607-624, December.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:8:p:607-624
    DOI: 10.1002/nav.21556
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    Cited by:

    1. Tamás Solymosi, 2019. "Weighted nucleoli and dually essential coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1087-1109, December.
    2. Zhanwen Shi & Erbao Cao & Kai Nie, 2023. "Capacity pooling games in crowdsourcing services," Electronic Commerce Research, Springer, vol. 23(2), pages 1007-1047, June.
    3. Jose A. García-Martínez & Ana Meca & G. Alexander Vergara, 2022. "Cooperative Purchasing with General Discount: A Game Theoretical Approach," Mathematics, MDPI, vol. 10(22), pages 1-20, November.
    4. Josep Maria Izquierdo & Carlos Rafels, 2020. "Core Allocations in Co-investment Problems," Group Decision and Negotiation, Springer, vol. 29(6), pages 1157-1180, December.
    5. Tamás Solymosi, 2019. "Weighted nucleoli and dually essential coalitions (extended version)," CERS-IE WORKING PAPERS 1914, Institute of Economics, Centre for Economic and Regional Studies.
    6. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).

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