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Cooperative and axiomatic approaches to the knapsack allocation problem

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  • 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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    Cited by:

    1. 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.
    2. 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..
    3. 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.

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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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