Carath\'eodory-type selection and random fixed point theorems for discontinuous correspondences
Anuj Bhowmik, Nicholas C. Yannelis
TL;DR
This paper develops new Carathéodory-type selection theorems for discontinuous correspondences and extends fixed point and equilibrium theorems to random and Bayesian contexts, broadening their applicability.
Contribution
It introduces novel Carathéodory-type selection theorems for discontinuous correspondences and generalizes fixed point and equilibrium theorems to stochastic settings.
Findings
New Carathéodory-type selection theorems for discontinuous correspondences
Extensions of fixed point theorems to random and Bayesian frameworks
Corollaries include and extend results by Kim-Prikry-Yannelis, Browder, Fan, and Nash.
Abstract
Research in Economics and Game theory has necessitated results on Carath\'eodory-type selections. In particular, one has to obtain Carath\'eodory type-selections from correspondences that need not be continuous (neither lower-semicontinuous nor upper-semicontinuous). We provide new theorems on Carath\'eodory 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.