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One-bound core games

Author

Listed:
  • Doudou Gong

    (Nanjing University of Science and Technology)

  • Bas Dietzenbacher

    (Maastricht University)

  • Hans Peters

    (Maastricht University)

Abstract

This paper introduces the new class of one-bound core games, where the core can be described by either a lower bound or an upper bound on the payoffs of the players, named lower bound core games and upper bound core games, respectively. We study the relation of the class of one-bound core games with several other classes of games and characterize the new class by the structure of the core and in terms of Davis-Maschler reduced games. We also provide explicit expressions and axiomatic characterizations of the nucleolus for one-bound core games, and show that the nucleolus coincides with the Shapley value and the $$\tau$$ τ -value when these games are convex.

Suggested Citation

  • Doudou Gong & Bas Dietzenbacher & Hans Peters, 2024. "One-bound core games," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 859-878, September.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:3:d:10.1007_s00182-024-00889-0
    DOI: 10.1007/s00182-024-00889-0
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    References listed on IDEAS

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    1. Kar, Anirban & Mitra, Manipushpak & Mutuswami, Suresh, 2009. "On the coincidence of the prenucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 16-25, January.
    2. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    3. A. van den Nouweland & P. Borm & W. van Golstein Brouwers & R. Groot Bruinderink & S. Tijs, 1996. "A Game Theoretic Approach to Problems in Telecommunication," Management Science, INFORMS, vol. 42(2), pages 294-303, February.
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    6. Doudou Gong & Bas Dietzenbacher & Hans Peters, 2022. "Reduced two-bound core games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(3), pages 447-457, December.
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    More about this item

    Keywords

    One-bound core games; Lower bound core games; Upper bound core games; Core; Nucleolus;
    All these keywords.

    JEL classification:

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

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