“The Division Problem with Voluntary Participation”

GUSTAVO BERGANTIÑOS, JORDI MASSÓ Y ALEJANDRO NEME

San Luis. Argentina

Jornada; 9º Jornadas Latinoamericano de Economía Teórica.; 2008

Instituto de matemática Aplicada-Universidad nacional de San Luis

Abstract: 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 find 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 efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.