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Probabilistic resource pooling games

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  • Loe Schlicher
  • Marco Slikker
  • Geert‐Jan van Houtum

Abstract

We study a setting with a single type of resource and with several players, each associated with a single resource (of this type). Unavailability of these resources comes unexpectedly and with player‐specific costs. Players can cooperate by reallocating the available resources to the ones that need the resources most and let those who suffer the least absorb all the costs. We address the cost savings allocation problem with concepts of cooperative game theory. In particular, we formulate a probabilistic resource pooling game and study them on various properties. We show that these games are not necessarily convex, do have non‐empty cores, and are totally balanced. The latter two are shown via an interesting relationship with Böhm‐Bawerk horse market games. Next, we present an intuitive class of allocation rules for which the resulting allocations are core members and study an allocation rule within this class of allocation rules with an appealing fairness property. Finally, we show that our results can be applied to a spare parts pooling situation.

Suggested Citation

  • Loe Schlicher & Marco Slikker & Geert‐Jan van Houtum, 2017. "Probabilistic resource pooling games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(7), pages 531-546, October.
    • Handle: RePEc:wly:navres:v:64:y:2017:i:7:p:531-546
    DOI: 10.1002/nav.21776
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    References listed on IDEAS

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    1. M. Guajardo & M. Rönnqvist, 2015. "Cost allocation in inventory pools of spare parts with service-differentiated demand classes," International Journal of Production Research, Taylor & Francis Journals, vol. 53(1), pages 220-237, January.
    2. Geert-Jan van Houtum & Bram Kranenburg, 2015. "Spare Parts Inventory Control under System Availability Constraints," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4899-7609-3, April.
    3. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    4. Albert Y. Ha, 1997. "Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales," Management Science, INFORMS, vol. 43(8), pages 1093-1103, August.
    5. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
    6. Wong, Hartanto & Oudheusden, Dirk Van & Cattrysse, Dirk, 2007. "Cost allocation in spare parts inventory pooling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(4), pages 370-386, July.
    7. Frank Karsten & Marco Slikker & Geert-Jan van Houtum, 2015. "Resource Pooling and Cost Allocation Among Independent Service Providers," Operations Research, INFORMS, vol. 63(2), pages 476-488, April.
    8. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
    9. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
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    Cited by:

    1. Loe Schlicher & Marco Slikker & Willem van Jaarsveld & Geert-Jan van Houtum, 2020. "Core Nonemptiness of Stratified Pooling Games: A Structured Markov Decision Process Approach," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1445-1465, November.
    2. Lotty E. Westerink‐Duijzer & Loe P. J. Schlicher & Marieke Musegaas, 2020. "Core Allocations for Cooperation Problems in Vaccination," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1720-1737, July.
    3. Westerink-Duijzer, L.E. & Schlicher, L.P.J. & Musegaas, M., 2019. "Fair allocations for cooperation problems in vaccination," Econometric Institute Research Papers EI2019-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. 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).
    5. Schlicher, L.P.J. & Musegaas, M. & Westerink-Duijzer, L.E., 2019. "Resource location games," Econometric Institute Research Papers EI2019-05, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Schlicher, Loe & Lurkin, Virginie, 2022. "Stable allocations for choice-based collaborative price setting," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1242-1254.
    7. Zhanwen Shi & Erbao Cao & Kai Nie, 2023. "Capacity pooling games in crowdsourcing services," Electronic Commerce Research, Springer, vol. 23(2), pages 1007-1047, June.

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