On the continuity of equilibrium and core correspondences in economies with differential information

Abstract

We study upper semi-continuity of the private core, the coarse core, and the Radner equilibrium correspondences for economies with differential information, with Boylan (1971) topology on agents' information fields.

Private Information: Similarity as Compatibility

“…This topology allows us to establish the upper semicontinuity of the private core. We also show that with private information restricted to finite partitions, the continuity of Radner equilibrium result of Einy et al (2004) is still true when the uniform continuity of the utility functions is relaxed.…”

“…The previous studies on the continuity of economic behavior with respect to information (Allen (1983) and Einy et al (2004)) used the topology introduced by Boylan (1971). This topology is generated by a pseudometric d that assigns a finite distance to any pair of σ-algebras, x and y, contained in B.…”

“…Upper semicontinuity of the Radner equilibrium set and of the private core can be established with the use of two technical lemmas from Einy et al (2004). The first states that the limit of informationally feasible functions is also informationally feasible.…”

“…In this general equilibrium framework, Einy, Haimanko, Moreno and Shitovitz (2004) We investigate the continuity properties of the private core and Walrasian equilibrium correspondences in differential information economies with a finite number of agents, where the private information of each agent is a finite partition of a compact and metrizable space of states of the world. This is the setting of the negative example of Einy et al (2004) that excludes upper semicontinuity of the private core correspondence.…”

“…This is the setting of the negative example of Einy et al (2004) that excludes upper semicontinuity of the private core correspondence. Our contribution is the introduction of a topology on information in which neighboring information fields are compatible, in the sense that they allow essentially the same contingent contracts.…”