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<p>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.</p>

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Rosen Games on Banach Spaces: Quasi-Convex Case

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Carlos Calderón,
  • John Cotrina,
  • Yboon García

摘要

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.