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Cooperative and axiomatic approaches to the knapsack allocation problem

Author

Listed:
  • Arribillaga, Pablo
  • Bergantiños, Gustavo
Abstract
In the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues should be considered. Firstly, to decide optimally the goods selected for the knapsack, which has been studied in many papers. Secondly, to divide the total revenue among the agents, which has been studied in few papers (including this one). We assign to each knapsack problem several cooperative games. For some of them we prove that the core is non-empty. Later, we follow the axiomatic approach. We propose two rules. The first one is based on the optimal solution of the knapsack problem. The second one is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules.

Suggested Citation

  • Arribillaga, Pablo & Bergantiños, Gustavo, 2019. "Cooperative and axiomatic approaches to the knapsack allocation problem," MPRA Paper 91719, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:91719
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    References listed on IDEAS

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    9. Bergantinos, Gustavo & Lorenzo-Freire, Silvia, 2008. ""Optimistic" weighted Shapley rules in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 185(1), pages 289-298, February.
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    15. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
    16. Jens Leth Hougaard & Hervé Moulin, 2018. "Sharing the cost of risky projects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 663-679, May.
    17. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2020. "Sharing the Revenues from Broadcasting Sport Events," Management Science, INFORMS, vol. 66(6), pages 2417-2431, June.
    18. Gustavo Bergantiños & Juan Vidal-Puga, 2007. "The optimistic TU game in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 223-239, October.
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    Cited by:

    1. Gustavo Berganti~nos & Juan D. Moreno-Ternero, 2024. "The Shapley index for music streaming platforms," Papers 2411.07166, arXiv.org.
    2. G. Bergantiños & Juan D. Moreno-Ternero, 2024. "Anonymity in sharing the revenues from broadcasting sports leagues," Annals of Operations Research, Springer, vol. 336(3), pages 1395-1417, May.
    3. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "On the difficulty of budget allocation in claims problems with indivisible items of different prices," ThE Papers 20/09, Department of Economic Theory and Economic History of the University of Granada..
    4. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.
    5. Yurun Ge & Lucas Bottcher & Tom Chou & Maria R. D'Orsogna, 2024. "A knapsack for collective decision-making," Papers 2409.13236, arXiv.org.

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    More about this item

    Keywords

    Knapsack problem; axiomatic; cooperative games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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