An equilibrium model with mixed federal structures.

*(English)*Zbl 1335.91059Summary: 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.

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.

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\textit{S. Weber} et al., Izv. Irkutsk. Gos. Univ., Ser. Mat. 8, 62--70 (2014; Zbl 1335.91059)

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