Abstract In this article a new interpretation of Aubin's fuzzy coalitions is given. This interpretation is based on associating each finite pure exchange economy with some large nonatomic economy. Then some connections between fuzzy core of finite economy and the core of associated nonatomic economy are established. From these results it is derived that for the case of convex preferences an allocation belonging to the fuzzy core is an equilibrium allocation. The assertion is not true in nonconvex case. We proceed by using the idea of J.P. Aubin — amplifying the class of coalitions in such a manner that an allocation unblocked by them is an equilibrium allocation also in the nonconvex case.
[1]
J. Aubin.
Mathematical methods of game and economic theory
,
1979
.
[2]
V. Tikhomirov,et al.
DUALITY OF CONVEX FUNCTIONS AND EXTREMUM PROBLEMS
,
1968
.
[3]
W. Hildenbrand.
Core and Equilibria of a Large Economy.
,
1974
.
[4]
Herbert E. Scarf,et al.
A LIMIT THEOREM ON THE CORE OF AN ECONOMY
,
1963,
Classics in Game Theory.
[5]
R. Aumann.
Markets with a continuum of traders
,
1964
.
[6]
M. Shubik,et al.
Convex structures and economic theory
,
1968
.