An Equilibrium Model with Mixed Federal Structures

This paper examines the problem of meeting an inelastic demand for public goods of club type in an economy with a finite number of agents, who exhibit different preferences regarding the choice of public projects. The choice problem is assumed to be multidimensional as there are several dimensions of a societal decision.
From the formal point of view, the problem can be summarized as follows. There are $n$ players, identified by points in a multidimensional space, who should be partitioned into a finite number of groups under the requirement that there exists no nonempty subset $S$ of players, each member of which strictly prefers (in terms of utilities) group $S$ to the group he was initially allocated.
Utilities which are inversely related to costs consist of two parts: monetary part (inversely proportional to the group's size), and the transportation part (distance from the location of a player to the point minimizing aggregate transportation cost within his group).
One cannot hope for a general result of existence of stable coalition structure even in a uni-dimensional setting. However, by allowing formation of several coalition structures, each pursuing a different facet of public decision, we obtain a very general existence result. Formally, this means that for each coalition there exists a balanced system of weights assigned to each of the dimensions of the public project.