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Reduced two-bound core games

Author

Listed:
  • 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. 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).
    2. 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.
    3. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    4. 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.
    5. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    6. 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.
    7. 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.
    8. 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.
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    More about this item

    JEL classification:

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

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