NTU-bankruptcy problems: consistency and the relative adjustment principle
- PDF / 498,362 Bytes
- 22 Pages / 439.37 x 666.142 pts Page_size
- 70 Downloads / 197 Views
NTU-bankruptcy problems: consistency and the relative adjustment principle Bas Dietzenbacher1 · Peter Borm2 · Arantza Estévez-Fernández3 Received: 14 March 2019 / Accepted: 14 October 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
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. Keywords NTU-bankruptcy problems · Consistency · Relative adjustment principle · Parametric bankruptcy rules · Adjusted bankruptcy rules JEL Classification C79 · D63 · D74
1 Introduction A bankruptcy problem with nontransferable utility, shortly an NTU-bankruptcy problem, arises when claimants have individual and incomparable claims on a set of attainable utility allocations. Bankruptcy rules assign to each such a bankruptcy problem a feasible utility allocation. NTU-bankruptcy problems form a natural gener-
B. Dietzenbacher: Support from the Basic Research Program of the National Research University Higher School of Economics is gratefully acknowledged.
B
Bas Dietzenbacher [email protected]
1
International Laboratory of Game Theory and Decision Making, National Research University Higher School of Economics, St. Petersburg, Russian Federation
2
Department of Econometrics and Operations Research, CentER, Tilburg University, Tilburg, The Netherlands
3
Department of Econometrics and Operations Research, Tinbergen Institute, VU University, Amsterdam, The Netherlands
123
B. Dietzenbacher et al.
alization of TU-bankruptcy problems where the assumption of linear and transferable utility is dropped. TU-bankruptcy problems are well-studied in the literature (cf. Thomson 2003, 2013, 2015) and the question arises whether and how bankruptcy theory can be extended to NTU-bankruptcy problems. However, this passage is in general fraught with difficulties. Orshan et al. (2003), and Dietzenbacher (2018), Estévez-Fernández et al. (2019) studied NTU-bankruptcy problems from a game theoretic perspective by defining an appropriate coalitional bankruptcy game and focusing on the structure of the core. Instead, we continue on the axiomatic approach of Dietzenbacher et al. (2016) by formulating some appropriate properties for bankruptcy rules and studying their implications. Dietzenbacher et al. (2016) explored proportionality, equality, and duality in the context of NTU-bankruptcy problems and introduced the proportional rule, the constrained relative equal awards rule, and the constrained relative equal losses rule. They extended axiomatic characterizations by
Data Loading...
