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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.

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  • 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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    8. 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.
    9. Artem Sedakov & Hao Sun, 2020. "The Relationship between the Core and the Modified Cores of a Dynamic Game," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
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    12. Ying Wang & Xiangyu Mao & Hashim Zameer, 2022. "Designing benefit distribution driven innovation strategy for local enterprises under the global value chain system," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(6), pages 2358-2373, September.
    13. van Zon, M. & Spliet, R. & van den Heuvel, W., 2021. "The effect of algorithm capabilities on cooperative games," Econometric Institute Research Papers EI2021-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    16. Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.
    17. Christoph Weissbart, 2018. "Decarbonization of Power Markets under Stability and Fairness: Do They Influence Efficiency?," ifo Working Paper Series 270, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    18. 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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