The Division Problem with Maximal Capacity Constraints

Resumo

The division problem consists of allocating a given amount of an homo- geneous 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 all divisions are feasible. In this paper we consider the division problem when each agent has a maximal capacity due to an objective and verifable feasibility constraint which imposes an upper bound on his share. Then each agent has a feasible interval of shares where his preferences are single-peaked. A rule has to propose to each agent a feasible share. We focus mainly on strategy-proof, e¢ cient and consistent rules and provide alternative characterizations of the extension of the uniform rule that deals explicitly with agents maximal capacity constraints.