A consistent talmudic rule for division problems with multiple references

Abstract

We consider an extension of the classic division problem with claims, division problems with multiple references. We show that the theory of cooperative games is able to provide a single-valued allocation rule for this class of problems. Moreover, this rule can be related with the Talmud rule for the classic division problem, as in Aumann and Maschler (J. Econ. Theory 36, 195-213, 1985). Finally, we establish the consistency and other basic properties of the rule.

A random arrival rule for division problems with multiple references

“…It is worth remarking that for two‐agent problems, the extended talmudic rule introduced in Hinojosa et al. () for division problems with multiple references coincides with the classic talmudic rule applied when each agent only takes into account the minimum of his references. In addition, the talmudic rule coincides with the random arrival rule for two agents.…”

“…Moreover, there are several links with the classic random arrival rule and with the extended talmudic rule proposed in Hinojosa et al. () that are established in the paper.…”

“…The following example, whose data have been extracted from Hinojosa et al. (), illustrates the behavior of the random arrival rule with multiple references. Example Consider the division problem , with three agents, and two references where .…”

“…Finally, Table shows the outcomes obtained for different values of the estate with the rule, the with , the extended talmudic rule (Hinojosa et al., ), and the two‐stage rule introduced in González‐Alcón et al. ().…”

Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update

“…Papers on the subject are by González-Alcón, Borm, and Hendrickx (2003), Calleja, Borm, and Hendrickx (2005), Borm, Carpente, Casas-Méndez, Hendrickx (2005), Moreno-Ternero (2009), and Bergantiños, Lorenzo, and Lorenzo-Freire (2010a, 2010b. Ju, Miyagawa and Sakai (2007) and Hinojosa, Mármol, and Sánchez (2012), also offer results that pertain to this model.…”