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An equilibrium model with mixed federal structures. (English) Zbl 1335.91059
Summary: 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.
##### MSC:
 91F10 History, political science 91B18 Public goods 91A80 Applications of game theory
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##### References:
 [1] Alesina, A.; Spolaore, E., On the number and size of nations, Quarterly Journal of Economics , 1027-1056, (1997) [2] Alesina, A.; Angeloni, I.; Etro, F., International unions, American Economic Review , 602-615, (2005) [3] Bogomolnaia, A.; Le Breton, M.; Savvateev, A., Stability of jurisdiction structures under the equal share and Median rules, Economic Theory , 523-543, (2008) · Zbl 1203.91081 [4] Casella, A., The role of market size in the formation of jurisdictions, Review of Economic Studies , 83-108, (2001) · Zbl 1013.91077 [5] Danilov, V.I., On the Scarf theorem (in Russian), Economics and Mathematical Methods , 3, 137-139, (1999) [6] Haimanko, O.; Le Breton, M.; Weber, S., Transfers in a polarized country: bridging the gap between efficiency and stability, Journal of Public Economics , 1277-1303, (2004) [7] J´ehiel, P.; Scotchmer, S., Constitutional rules of exclusion in jurisdiction formation, Review of Economic Studies , 393-413, (2001) · Zbl 0980.91070 [8] Makarov, V.L., Calculus of institutions (in Russian), Economics and Mathematical Methods , 2, 14-32, (2003) · Zbl 1075.91522 [9] Scarf, H.E., The core of an N-person game, Econometrica , 50-69, (1967) · Zbl 0183.24003
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