A proof of the existence of private core allocations is provided for an exchange economy " in which consumers and commodities are both infinite in number, supposing however that only finitely many types
can be distinguished among traders.
It is obtained passing through a suitably associated discrete setting where a preliminary result— which is interesting in itself—is proved: in every generalized replica of an economy E with asymmetric information and a finite number of traders there is a private core allocation
which treats agents of the same type equally.
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