The division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will …nd acceptable any share they are assigned to. In this paper we consider the division problem when agents’participation is voluntary. Each agent has an acceptable interval of shares where his preferences are single-peaked. A rule has to propose to each agent either an acceptable share or the zero share because otherwise, he would prefer to exclude himself and leave with the zero share; this would require to reassign the remaining agents’shares. We study a subclass of e¢ cient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents’voluntary participation. We thank Bettina Klaus for helpful comments. The work of G. Bergantiños is partially supported by research grant ECO2008-03484-C02-01 from the Spanish Ministry of Science and Innovation and FEDER. Support for the research of J. Massó was received through the prize “ICREA Acadèmia” for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of the Barcelona Graduate School of Economics, where he is an A¢ liated Professor, through its Research Recognition Programme. His work is also supported by the Spanish Ministry of Science and Innovation through grants ECO2008-04756 (Grupo Consolidado-C) and CONSOLIDER-INGENIO 2010 (CDS2006-00016), and by the Generalitat de Catalunya through grant SGR2005-00454. The work of A. Neme is partially supported by the Universidad Nacional de San Luis through grant 319502, by the Consejo Nacional de Investigaciones Cientí…cas y Técnicas CONICET, through grant PICT-02114, and by the Agencia Nacional de Promoción Cientí…ca y Técnica, through grant 03-10814. yResearch Group in Economic Analysis. Facultade de Económicas, Universidade de Vigo. 36310, Vigo (Pontevedra), Spain. E-mail: [email protected] zDepartament d’Economia i d’Història Econòmica and CODE. Universitat Autònoma de Barcelona. 08193, Bellaterra (Barcelona), Spain. E-mail: [email protected] xInstituto de Matemática Aplicada de San Luis. Universidad Nacional de San Luis and CONICET. Ejército de los Andes 950. 5700, San Luis, Argentina. E-mail: [email protected] Journal of Economic Literature Classi…cation Number: D71.