Continuity properties of the private core
نویسندگان
چکیده
Let (Ek)k∈N be a sequence of differential information economies, converging to a limit differential information economy E∞ (written as Ek ⇒ E∞). Denote by C (Ek) the set of all -private core allocations, ≥ 0 (for = 0 we get the private core of Yannelis (1991), denoted by C(Ek)). Under appropriate conditions, we prove the following stability results: (1) (upper semicontinuity): if Ek ⇒ E∞, fk ∈ C(Ek), and if fk → f∞ L1-weakly, then f∞ ∈ C(E∞). (2) (lower semicontinuity): if Ek ⇒ E∞, f∞ ∈ C(E∞), > 0, then there exist fk ∈ C (Ek), with fk → f∞ L1-weakly.
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