The Nucleolus Of The Bankruptcy Problem By Hydraulic Rationing
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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Volume (Year): 14 (2012)
Issue (Month): 01 ()
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- 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.
- 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.
- Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Juan de Dios Moreno Ternero & Antonio Villar Notario, 2003.
"The Talmud Rule And The Securement Of Agents? Awards,"
Working Papers. Serie AD
2003-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- 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.
- 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.
- Toru Hokari & William Thomson, 2007.
"On properties of division rules lifted by bilateral consistency,"
RCER Working Papers
536, University of Rochester - Center for Economic Research (RCER).
- 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.
- 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.
- Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
- 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.
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