The minimal overlap rule: restrictions on mergers for creditors' consensus
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.
scientific article; zbMATH DE number 6352468