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The Nucleolus Of The Bankruptcy Problem By Hydraulic Rationing

  • TAMÁS FLEINER

    ()

    (Budapest University of Technology and Economics, Department of Computer Science and Information Theory, H-1117 Budapest, Magyar tudósok körútja 2, Hungary)

  • BALÁZS SZIKLAI

    ()

    (Institute of Economics, Research Center for Economic and Regional Studies, Hungarian Academy of Sciences, H-1112, Budapest, Budaörsi út 45, Hungary)

In this note, we give a straightforward and elementary proof of a theorem by Aumann and Maschler stating that in the well-known bankruptcy problem, the so-called CG-consistent solution described by the Talmud represents the nucleolus of the corresponding coalitional game. The proof nicely fits into the hydraulic rationing framework proposed by Kaminski. We point out further interesting properties in connection with this framework.

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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 14 (2012)
Issue (Month): 01 ()
Pages: 1250007-1-1250007-11

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Handle: RePEc:wsi:igtrxx:v:14:y:2012:i:01:p:1250007-1-1250007-11
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  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. Hokari, Toru & Thomson, William, 2008. "On properties of division rules lifted by bilateral consistency," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1057-1071, December.
  3. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
  4. Benoit, Jean-Pierre, 1997. "The Nucleolus Is Contested-Garment-Consistent: A Direct Proof," Journal of Economic Theory, Elsevier, vol. 77(1), pages 192-196, November.
  5. Benoit, Jean-Pierre, 1997. "The Nucleolus is Contested-Garment-Consistent: A Direct Proof," Working Papers 97-12, C.V. Starr Center for Applied Economics, New York University.
  6. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
  7. 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.
  8. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
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