Conditional expectation of Banach valued correspondences and economic applications

Wei He and Yeneng Sun

Journal of Mathematical Economics, 2022, vol. 101, issue C

Abstract: We present some regularity properties (convexity, weak/weak∗ compactness and preservation of weak/weak∗ upper hemicontinuity) for Bochner/Gel′fand conditional expectation of Banach valued correspondences under the nowhere equivalence condition. These regularity properties for Bochner/Gel′fand integral of Banach valued correspondences are obtained as corollaries. We prove the necessity of the nowhere equivalence condition for any of these properties to hold. Economic applications, including a general class of large games and abstract economies with asymmetric information, are discussed.

Keywords: Conditional expectation of Banach valued correspondence; Integral of Banach valued correspondence; Nowhere equivalence; Nash equilibrium (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:101:y:2022:i:c:s0304406822000477

DOI: 10.1016/j.jmateco.2022.102698

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