Carathéodory-type selection and random fixed point theorems for discontinuous correspondences

Anuj Bhowmik; Nicholas C Yannelis

doi:10.48550/arxiv.2508.18997

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Carathéodory-type selection and random fixed point theorems for discontinuous correspondences

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Carathéodory-type selection and random fixed point theorems for discontinuous correspondences

Anuj Bhowmik and Nicholas C Yannelis

ArXiv.org

Cornell University

08/26/2025

DOI: 10.48550/arxiv.2508.18997

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Research in Economics and Game theory has necessitated results on Carathéodory-type selections. In particular, one has to obtain Carathéodory type-selections from correspondences that need not be continuous (neither lower-semicontinuous nor upper-semicontinuous). We provide new theorems on Carathéodory type-selections that include as corollaries the results in Kim-Prikry-Yannelis \cite{KPY:87}. We also, obtain new random fixed-point theorems, random maximal elements, random (Nash) equilibrium and Bayesian equilibrium extending and generalizing theorems of Browder \cite{Browder:68}, Fan \cite{Fan:52} and Nash \cite{Nash}, among others.

Mathematics - General Topology

Mathematics - Probability

Details

Title: Subtitle: Carathéodory-type selection and random fixed point theorems for discontinuous correspondences
Creators: Anuj Bhowmik
Nicholas C Yannelis
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2508.18997
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 08/26/2025
Academic Unit: Economics
Record Identifier: 9984949229902771

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