Rosen Games on Banach Spaces: Quasi-Convex Case

Abstract

We study the generalized Nash game proposed by Rosen, which involves strategy sets coupled across players through a shared constraint. We demonstrate a reduction to a classical game, allowing Rosen’s result to be deduced from the work of Arrow and Debreu. Additionally, we establish an existence result under the quasi-convexity assumption in Banach spaces. New existence results are also provided for the non-compact case under coerciveness conditions. Finally, an abstract economy is considered as an application.