Abstract
In this paper, we consider a bankruptcy problem with the additional constraint that the estate has to be assigned in integer unities; differently from the approaches by other authors, we allow for non-integer claims. This situation poses new questions on the existence and the uniqueness of the solution. We propose a new solution method that leads to the “box solution”, for which uniqueness may be guaranteed introducing a ranking on the claimants. Some examples complete the paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The algorithm has been developed in Matlab and the test has been run on a Notebook with a AMD E-450 APU processor, 1.65 GPU Clock, 4 Gb Ram.
References
Balinski ML, Young HP (1977) On Huntington methods of apportionment. SIAM J Appl Math 33:607–618
Bebchuck LA, Fried JM (1996) The uneasy case for the priority of secured claims in bankruptcy. Yale Law J 105:857–934
Branzei R, Ferrari G, Fragnelli V, Tijs SH (2008) A flow approach to bankruptcy problems. AUCO Econ Czech Rev 2:146–153
Branzei R, Ferrari G, Fragnelli V, Tijs SH (2011) A bonus-malus approach to project management. Cent Eur J Oper Res 19:495–512
Calleja P, Borm P, Hendrickx R (2005) Multi-issue allocation situations. Eur J Oper Res 164:730–747
Carpente L, Casas B, Gozalvez J, Llorca N, Pulido M, Sanchez-Soriano J (2008) How to divide a cake when people have different metabolism? Math Meth Oper Res 78:361–371
Chen S (2012) Systematic favorability in claims problems with indivisibilities. Working paper
Curiel IJ, Maschler M, Tijs SH (1987) Bankruptcy games. Math Methods Oper Res 31(5):A143–A159
Gozalvez J, Lucas-Estañ MC, Sanchez-Soriano J (2007) User QoS-based multi-channel assignment schemes under multimedia traffic conditions. In: Proceedings of 4th international symposium on wireless communications systems (ISWCS 2007), Trondheim, pp 113–117
Herrero C, Martinez R (2004) Egalitarian rules in claims problems with indivisible goods. IVIE-WP-AD 2004-20, pp 1–24
Herrero C, Martinez R (2008a) Up methods in the allocation of indivisibilities when preferences are single-peaked. TOP 16:272–283
Herrero C, Martinez R (2008b) Balanced allocation methods for claims problems with indivisibilities. Soc Choice Welf 30:603–617
Herrero C, Martinez R (2011) Allocation problems with indivisibilities when preferences are single-peaked. SERIEs: J Span Econ Assoc 2:453–467
Herrero C, Maschler M, Villar A (1999) Individual rights and collective responsibility: the rights-egalitarian solution. Math Soc Sci 37(1):59–77
Herrero C, Villar A (2001) The three musketeers: four classical solutions to bankruptcy problems. Math Soc Sci 42:307–328
Kaminski MM (2000) ‘Hydraulic’ rationing. Math Soc Sci 40:131–155
Lucas-Estañ MC, Gozalvez J, Sanchez-Soriano J, Pulido M, Calabuig D (2007) Multi-channel radio resource distribution policies in heterogeneous traffic scenarios. In: Proceedings of the IEEE 66th vehicular technology conference (VTC2007-Fall), Baltimore, pp 1674–1678
Lucas-Estañ MC, Gozalvez J, Sanchez-Soriano J (2012) Bankruptcy-based radio resource management for multimedia mobile networks. Trans Emerg Telecommun Technol 23:186–201
Moreno-Ternero JD (2009) Proportional rule for multi-issue bankruptcy problems. Econ Bull 29(1):483–490
Moulin H (2000) Priority rules and other asymmetric rationing methods. Econometrica 68:643–684
Orshan G, Valenciano F, Zarzuelo JM (2003) The bilateral consistent prekernel, the core and NTU bankruptcy problems. Math Oper Res 28(2):268–282
Pulido M, Sanchez-Soriano J, Llorca N (2002) Game theory techniques for university management: an extended bankruptcy model. Ann Oper Res 109:129–142
Schwarcz SL (1997) The easy case for the priority of secured claims in bankruptcy. Duke Law J 47:425–489
Thomson W (2003) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45:249–297
Young HP (1994) Equity, in theory and practice. Princeton University Press, Princeton
Acknowledgments
The authors are grateful to two anonymous Referees for their remarks that lead to a real improvement.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fragnelli, V., Gagliardo, S. & Gastaldi, F. Integer solutions to bankruptcy problems with non-integer claims. TOP 22, 892–933 (2014). https://doi.org/10.1007/s11750-013-0304-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-013-0304-x