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Computing core allocations in cooperative games with an application to cooperative procurement

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  • Drechsel, J.
  • Kimms, A.

Abstract

Cooperative game theory defines several concepts for distributing outcome shares in a cooperative game with transferable utilities. One of the most famous solution concepts is the core which defines a set of outcome allocations that are stable such that no coalition has an incentive to leave the grand coalition. In this paper we propose a general procedure to compute a core element (or to detect that no core allocation exists) which is based on mathematical programming techniques. The procedure proposed in this paper can be applied to a wide class of cooperative games where the characteristic function is given by the optimum objective function value of a complex optimization problem. For cooperative procurement, which is an example from the field of supply chain management where some literature on the core concept already exists, we prove the applicability and provide computational results to demonstrate that games with 150 players can be handled.

Suggested Citation

  • Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
  • Handle: RePEc:eee:proeco:v:128:y:2010:i:1:p:310-321
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    Cited by:

    1. Lozano, S. & Moreno, P. & Adenso-Díaz, B. & Algaba, E., 2013. "Cooperative game theory approach to allocating benefits of horizontal cooperation," European Journal of Operational Research, Elsevier, vol. 229(2), pages 444-452.
    2. Mohebbi, Shima & Li, Xueping, 2015. "Coalitional game theory approach to modeling suppliers' collaboration in supply networks," International Journal of Production Economics, Elsevier, vol. 169(C), pages 333-342.
    3. Kimms, A. & Kozeletskyi, I., 2016. "Core-based cost allocation in the cooperative traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 248(3), pages 910-916.
    4. Guajardo, Mario & Rönnqvist, Mikael, 2015. "Operations research models for coalition structure in collaborative logistics," European Journal of Operational Research, Elsevier, vol. 240(1), pages 147-159.
    5. Mohammaditabar, Davood & Ghodsypour, Seyed Hassan & Hafezalkotob, Ashkan, 2016. "A game theoretic analysis in capacity-constrained supplier-selection and cooperation by considering the total supply chain inventory costs," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 87-97.
    6. Kimms, Alf & Çetiner, Demet, 2012. "Approximate nucleolus-based revenue sharing in airline alliances," European Journal of Operational Research, Elsevier, vol. 220(2), pages 510-521.
    7. Palsule-Desai, Omkar D. & Tirupati, Devanath & Chandra, Pankaj, 2013. "Stability issues in supply chain networks: Implications for coordination mechanisms," International Journal of Production Economics, Elsevier, vol. 142(1), pages 179-193.
    8. Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.
    9. Xiaozhou Xu & Shenle Pan & Eric Ballot, 2013. "A sharing mechanism for superadditive and non-superadditive logistics cooperation," Post-Print halshs-00876006, HAL.

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