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The Aggregate-Monotonic Core

Author

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  • Pedro Calleja
  • Carles Rafels
  • Stef Tijs

Abstract

The main objective of the paper is to study the locus of all core selection and aggregate monotonic point solutions of a TU-game: the aggregate-monotonic core. Furthermore, we characterize the class of games for which the core and the aggregate-monotonic core coincide. Finally, we introduce a new family of rules for TU-games which satisfy core selection and aggregate monotonicity.

Suggested Citation

  • Pedro Calleja & Carles Rafels & Stef Tijs, 2006. "The Aggregate-Monotonic Core," Working Papers 280, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:280
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    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/280.pdf
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    References listed on IDEAS

    as
    1. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    2. J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 211-227.
    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. Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 133-137.
    5. David Housman & (*), Lori Clark, 1998. "Note Core and monotonic allocation methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 611-616.
    6. J. Arin & V. Feltkamp, 2005. "Monotonicity properties of the nucleolus on the domain of veto balanced games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 331-341, December.
    7. Ichiishi, T, 1990. "Comparative Cooperative Game Theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 139-152.
    8. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
    9. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    10. Kannai, Yakar, 1992. "The core and balancedness," 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 12, pages 355-395, Elsevier.
    11. ICHIISHI, Tatsuro, 1990. "Comparative cooperative game theory," LIDAM Reprints CORE 903, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Moulin, H, 1990. "Cores and Large Cores When Population Varies," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 219-232.
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