The minimal overlap rule: restrictions on mergers for creditors' consensus
type: Item
instance of: scholarly article
title: The minimal overlap rule: restrictions on mergers for creditors' consensus
zbMATH Open document ID: 1309.91078
author: José Alcalde
author: María del Carmen Marco-Gil
author: José A. Silva-Reus
published in: Top
publication date: 2014-10-08T00:00:00Z
full work available at URL: qmetwp1201.pdf
review text: The avoidance of bankruptcy has been suggested as a plausible motive for merging. In this context the authors try to find out sharing rules for bankruptcy situations that are not affected by business alliances. To deal with this question they formalize general rationing situations as bankruptcy and use an axiomatic approach. In this framework, neutrality against mergers is called additivity. \textit{G. Bergantiños} and \textit{L. Méndez-Naya} [``Additivity in bankruptcy problems and in allocation problems'', Span. Econ. Rev. 3, No. 3, 223--229 (2001; \url{doi:10.1007/PL00011444})] concluded that there is no bankruptcy rule satisfying additivity but, considering a very restrictive family of bankruptcy problems. The previous impossibility results shows that additivity is a very demanding axiom. This paper presents a weak notion of additivity, that they call \(\mu\)-additivity. The authors' main result establishes that the minimal overlap rule, introduced by \textit{B. O'Neill} [Math. Soc. Sci. 2, 345--371 (1982; Zbl 0489.90090)], is the only rule for which \(\mu\)-additivity is compatible with equal treatment of equals and continuity, two properties which have been widely justified in the literature for bankruptcy problems.
Mathematics Subject Classification ID: 91B32
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 6352468
zbMATH Keywords: bankruptcy
zbMATH Keywords: additivity
zbMATH Keywords: \(\mu\)-additivity
zbMATH Keywords: minimal overlap rule
reviewed by: Ahmed Hegazi
MaRDI profile type: Publication
OpenAlex ID: W2067089982
cites work: The minimal overlap rule revisited
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DOI: 10.1007/S11750-012-0262-8
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description: scientific article; zbMATH DE number 6352468