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Cooperative and axiomatic approaches to the knapsack allocation problem

Author

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  • R. Pablo Arribillaga

    (Universidad Nacional de San Luis and CONICET)

  • G. Bergantiños

    (Universidade de Vigo, ECOSOT)

Abstract

In the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues must be considered. The first is to decide optimally what goods to select for the knapsack. This issue has been studied in many papers in the literature on Operations Research and Management Science. The second issue is to divide the total revenue among the agents. This issue has been studied in only a few papers, and this is one of them. For each knapsack problem we consider three associated cooperative games. One of them (the pessimistic game) has already been considered in the literature. The other two (realistic and optimistic games) are defined in this paper. The pessimistic and realistic games have non-empty cores but the core of the optimistic game could be empty. We then follow the axiomatic approach. We propose two rules: The first is based on the optimal solution of the knapsack problem. The second is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules.

Suggested Citation

  • R. Pablo Arribillaga & G. Bergantiños, 2022. "Cooperative and axiomatic approaches to the knapsack allocation problem," Annals of Operations Research, Springer, vol. 318(2), pages 805-830, November.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:2:d:10.1007_s10479-021-04315-6
    DOI: 10.1007/s10479-021-04315-6
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    2. Gustavo Bergantinos & Juan D. Moreno-Ternero, 2023. "Anonymity in sharing the revenues from broadcasting sports leagues," Papers 2303.17897, arXiv.org.
    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..

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    More about this item

    Keywords

    Knapsack problem; Axiomatic approach; Cooperative games;
    All these keywords.

    JEL classification:

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

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