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Reduced two-bound core games

Author

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  • Gong, Doudou

    (RS: GSBE other - not theme-related research, Quantitative Economics)

  • Dietzenbacher, Bas

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory)

  • Peters, Hans

    (QE Math. Economics & Game Theory, RS: GSBE other - not theme-related research)

Abstract

This paper studies Davis-Maschler reduced games of two-bound core games and shows that all these reduced games with respect to core elements are two-bound core games with the same pair of bounds. Based on associated reduced game properties, we axiomatically characterize the core, the nucleolus, and the egalitarian core for two-bound core games. Moreover, we show that the egalitarian core for two-bound core games is single-valued and we provide an explicit expression.

Suggested Citation

  • Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "Reduced two-bound core games," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2022001
    DOI: 10.26481/umagsb.2022001
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    References listed on IDEAS

    as
    1. Peleg, B, 1987. "On the Reduced Game Property and Its Converse: A Correction," International Journal of Game Theory, Springer;Game Theory Society, vol. 16(4), pages 290-290.
    2. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    3. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 153-169.
    5. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    6. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 187-193.
    7. Robert J. Aumann, 2025. "Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 9, pages 219-242, World Scientific Publishing Co. Pte. Ltd..
    8. Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005. "The core cover in relation to the nucleolus and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
    9. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
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    Cited by:

    1. 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.

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    JEL classification:

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

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