Equitable and Decentralized Solution for the Allocation of Indivisible Objects

In this paper we consider a model, where at most one object is allocated to each individual, with no two individuals sharing one or more objects, and possibly some allocations being defined infeasible. We propose a weaker sufficient condition than the one suggested by Herreiner and Puppe (2002) for a balanced solution to be an outcome of the DDP, for some ordering of the individuals. Further, we define another method called the first encounter descending demand procedure (FEDDP), which in the unrestricted case, where the feasible set consists of all allocations where no two individuals share an object, can be used to obtain every balanced allocation. We also show in this paper, that it is possible for an allocation in a housing market to be balanced without belonging to the core and for an allocation to belong to the core in spite of not being balanced.