Abstract
This paper axiomatically studies bankruptcy problems with nontransferable utility by focusing on generalizations of consistency and the contested garment principle. On the one hand, we discuss several consistency notions and introduce the class of parametric bankruptcy rules which contains the proportional rule, the constrained relative equal awards rule, and the constrained relative equal losses rule. On the other hand, we introduce the class of adjusted bankruptcy rules and characterize the relative adjustment principle by truncation invariance, minimal rights first, and a weak form of relative symmetry.
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Notes
Alternatively, one can interpret a bankruptcy problem with nontransferable utility as a bargaining problem with claims (cf. Chun and Thomson 1992) where the disagreement point equals the zero vector, or as a Nash rationing problem (cf. Mariotti and Villar 2005) where the admissible allocations are nonnegative. Contrary to these models, we allow for a nonconvex estate and claims which exceed the maximal individual payoffs within the estate.
This type of theorem can be formulated for any bankruptcy rule satisfying bilateral consistency and converse consistency.
Peters et al. (1994) introduced a similar property for bargaining solutions.
For an arbitrary number of claimants, this formula corresponds to the adjusted proportional rule.
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B. Dietzenbacher: Support from the Basic Research Program of the National Research University Higher School of Economics is gratefully acknowledged.
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Dietzenbacher, B., Borm, P. & Estévez-Fernández, A. NTU-bankruptcy problems: consistency and the relative adjustment principle. Rev Econ Design 24, 101–122 (2020). https://doi.org/10.1007/s10058-019-00227-x
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DOI: https://doi.org/10.1007/s10058-019-00227-x
Keywords
- NTU-bankruptcy problems
- Consistency
- Relative adjustment principle
- Parametric bankruptcy rules
- Adjusted bankruptcy rules