Rosen Games on Banach Spaces: Quasi-Convex Case

Calderón C.; Cotrina J.; García Y. · Set-Valued and Variational Analysis (2025) · DOI: 10.1007/s11228-025-00748-4

Resumen

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. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.

Instituciones: Universidad del Pacífico