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An axiomatization of the kernel for TU games through reduced game monotonicity and reduced dominance

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  • Theo Driessen
  • Cheng-Cheng Hu

Abstract

In the framework of transferable utility games, we modify the 2-person Davis–Maschler reduced game to ensure non-emptiness (NE) of the imputation set of the adapted 2-person reduced game. Based on the modification, we propose two new axioms: reduced game monotonicity (RGM) and reduced dominance (RD). Using RGM, RD, NE, Covariance under strategic equivalence, Equal treatment property and Pareto optimality, we are able to characterize the kernel. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Theo Driessen & Cheng-Cheng Hu, 2013. "An axiomatization of the kernel for TU games through reduced game monotonicity and reduced dominance," Theory and Decision, Springer, vol. 74(1), pages 1-12, January.
    • Handle: RePEc:kap:theord:v:74:y:2013:i:1:p:1-12
    DOI: 10.1007/s11238-012-9344-1
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. 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).
    3. 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.
    4. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667, Elsevier.
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    More about this item

    Keywords

    Cooperative game; Kernel; Reduced game; Monotonicity; Dominance; C71;
    All these keywords.

    JEL classification:

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

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