Abstract
Pulido et al. (Annals Oper Res 158:133–141, 2008) present an extension of the classical bankruptcy problem (O’Neill in Math Social Sci 2:345–371, 1982) where the involved agents have, apart from the claims vector, an additional reference vector. To analyze this extended problem, they propose the extreme and the diagonal approaches, both of them restricted to the case in which the reference vector is lower than the claims vector. We note that if the claims and the reference vectors are interchanged, the allocation proposed by the extreme approach varies. Therefore, by introducing the idea of impartiality, in the current approach, we propose an extension of their model in which no relation is assumed between the claims and reference vectors.
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Notes
As usual, \(\left( x_{i},\mathbf {y}_{-i}\right) \) denotes the vector obtained from \(\mathbf {x}\) and \(\mathbf {y},\) so that the \(i-\)component is \(x_i\) and the remainder components are the corresponding ones in vector \(\mathbf {y}.\)
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Acknowledgments
We would like to thank specially two anonymous reviewers and the editor of this journal for all their very useful suggestions. The usual caveat applies. A. Osorio and J. E. Peris gratefully acknowledge financial support from Spanish Ministry of Economy and Competitiveness under projects ECO2011-24200 and ECO2013-43119, respectively.
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Giménez-Gómez, JM., Osório, A. & Peris, J.E. Bankruptcy problems with two references: an impartial compromise. TOP 24, 131–142 (2016). https://doi.org/10.1007/s11750-015-0381-0
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DOI: https://doi.org/10.1007/s11750-015-0381-0