2023/08/22 by Conrad Kosowsky, Kosowsky, Conrad
Economics, Econometrics and Finance · Mathematics · #Advanced Topology and Set Theory #Economic theories and models #FOS: Economics and business #Mathematical and Theoretical Analysis #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2308.11597
openalex publication_date 2023/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, I prove the existence of a pure-strategy Nash equilibrium for a large class of games with nonconvex strategy spaces. Specifically, if each player's strategies form a compact, connected Euclidean neighborhood retract and if all best-response correspondences are null-homotopic, then the game has a pure-strategy Nash equilibrium. As an application, I show how this result can prove the fundamental theorem of algebra.