Individually rational rules for the division problem when the number of units to be allotted is endogenous

Abstract

Altres ajus: The work of G. Bergantiños is partially supported by grants ECO2014-52616-R and ECO2017-82241-R from the Spanish Ministry of Economy and Competitiveness and ED431B 2019/34 from "Xunta de Galicia". J. Massó and A. Neme acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through grant ECO2014-5305, and J. Massó through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563) and from the Generalitat de Catalunya, through grant SGR2014-515. The paper was partly written while J. Massó was visiting the Department of Economics at Stanford University and acknowledges its hospitality as well as financial support received from the Spanish Ministry of Education, Culture and Sport, through project PR2015-00408. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through grant PIP 112-200801-00655.

Altres ajuts: ED431B 2019/34

Altres ajuts: SEV-2015-0563

We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and efficient rules, whenever agents' preferences are symmetric single-peaked on the set of possible allotments. The two rules are in addition envy-free, but they differ on wether envy-freeness is considered on losses or on awards. Our main result states that (i) the constrained equal losses rule is the unique individually rational and efficient rule that satisfies justified envy-freeness on losses and (ii) the constrained equal awards rule is the unique individually rational and efficient rule that satisfies envy-freeness on awards.