Characterizing NTU-bankruptcy rules using bargaining axioms
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Characterizing NTU-bankruptcy rules using bargaining axioms Bas Dietzenbacher1
· Hans Peters1
Accepted: 5 October 2020 © The Author(s) 2020
Abstract This paper takes an axiomatic bargaining approach to bankruptcy problems with nontransferable utility, by using properties from bargaining theory in order to characterize bankruptcy rules. In particular, we derive new axiomatic characterizations of the proportional rule, the truncated proportional rule, and the constrained relative equal awards rule, using properties which concern changes in the estate or in the claims. Keywords NTU-bankruptcy problem · Axiomatic analysis · Bargaining theory JEL Classification C78 · D74
1 Introduction In a bankruptcy problem with nontransferable utility, claimants have incompatible claims on an insufficient estate, which is represented by a set of attainable utility allocations. Such bankruptcy problems arise when claimants have individual utility functions over their monetary payoffs. Bankruptcy rules assign to any such bankruptcy problem a feasible utility allocation, i.e., an allocation for which the individual utility payoffs are bounded by the corresponding claims. On the one hand, bankruptcy problems with nontransferable utility generalize monetary bankruptcy problems, as introduced by O’Neill (1982). On the other hand, they can be considered as bargaining problems with claims (cf. Chun and Thomson 1992) under a somewhat different interpretation. Orshan et al. (2003), Dietzenbacher (2018), and Estévez-Fernández et al. (2020) took a game theoretic approach to bankruptcy problems with nontransferable utility by defining an appropriate coalitional bankruptcy game and focusing on the structure of the core. Moreover, Dietzenbacher (2018) showed that the class of game theoretic bankruptcy rules coincides with the class of bankruptcy rules satisfying truncation invariance, i.e., invariance under truncation of the claims by the estate.
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Bas Dietzenbacher [email protected] Hans Peters [email protected]
1
Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands
123
Annals of Operations Research
Recently, Dietzenbacher et al. (2020a, b) took an axiomatic approach to bankruptcy problems with nontransferable utility, by characterizing bankruptcy rules in terms of adequately generalized properties from bankruptcy theory. To explore the proportional rule, the truncated proportional rule, and the constrained relative equal awards rule, they proposed the relative symmetry axiom, which imposes relatively equal treatment of relatively equal claimants. This paper takes an axiomatic bargaining approach to bankruptcy problems with nontransferable utility by characterizing bankruptcy rules using properties from bargaining theory. Similar to Chun and Thomson (1992), we interpret the estate of a bankruptcy problem as the feasible set of a bargaining problem, as introduced by Nash (1950), which is enriched by a claims vector. However, we adopt the standard assumption from ba
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