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Enjoying cooperative games: The R package GameTheory

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  • Cano-Berlanga, Sebastián
  • Giménez-Gómez, José-Manuel
  • Vilella, Cori

Abstract

This paper focuses on cooperative games with transferable utility. We propose the computation of three solutions, the Shapley value for n agents, the nucleolus with a maximum of four agents and the per capita nucleolus. The current approach is also focused on conflicting claims problems, a particular case of coalitional games. We provide the computation of the most well-known and used claims solutions: the proportional, the constrained equal awards, the constrained equal losses, the Talmud, the random arrival and the adjusted proportional rules.

Suggested Citation

  • Cano-Berlanga, Sebastián & Giménez-Gómez, José-Manuel & Vilella, Cori, 2017. "Enjoying cooperative games: The R package GameTheory," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 381-393.
    • Handle: RePEc:eee:apmaco:v:305:y:2017:i:c:p:381-393
    DOI: 10.1016/j.amc.2017.02.010
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    Cited by:

    1. Mêgnigbêto, Eustache, 2018. "Modelling the Triple Helix of university-industry-government relationships with game theory: Core, Shapley value and nucleolus as indicators of synergy within an innovation system," Journal of Informetrics, Elsevier, vol. 12(4), pages 1118-1132.
    2. P. Giovani Palafox-Alcantar & Dexter V. L. Hunt & Chris D. F. Rogers, 2020. "A Hybrid Methodology to Study Stakeholder Cooperation in Circular Economy Waste Management of Cities," Energies, MDPI, vol. 13(7), pages 1-30, April.
    3. Miguel A. Ortiz Acuña & Adiel T. Almeida Filho & Francisco S. Ramos, 2024. "Modelling the triple helix system innovation of the main economies from Latin America: a coalitional game theory approach," Scientometrics, Springer;Akadémiai Kiadó, vol. 129(6), pages 3245-3270, June.
    4. Fatemeh Babaei & Hamidreza Navidi & Stefano Moretti, 2022. "A bankruptcy approach to solve the fixed cost allocation problem in transport systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 332-358, July.

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    More about this item

    Keywords

    Cooperative game; Shapley value; Nucleolus; Claims problem; Bankruptcy;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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