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<p>Generalized games with non-ordered preferences extend the well-known generalized Nash equilibrium problems to the case where preferences of players are not representable by utility functions. In this article, we employ tools from variational analysis to study these games. By solving an auxiliary variational inequality, we ensure the presence of an equilibrium for jointly convex generalized games in which the joint constraint sets are not necessarily bounded. Subsequently, we utilize a quasi-variational reformulation of generalized games to show the existence of equilibrium for generalized games in which the constraint maps may admit unbounded values. These existence results are proved by relaxing the convexity assumption on the preferences of players. Finally, we apply the derived results to ensure the existence of equilibrium for the Arrow-Debreu production economy.</p>

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Existence Results on Generalized Games with Unbounded Constraints Through Variational Reformulation

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • Asrifa Sultana,
  • Shivani Valecha

摘要

Generalized games with non-ordered preferences extend the well-known generalized Nash equilibrium problems to the case where preferences of players are not representable by utility functions. In this article, we employ tools from variational analysis to study these games. By solving an auxiliary variational inequality, we ensure the presence of an equilibrium for jointly convex generalized games in which the joint constraint sets are not necessarily bounded. Subsequently, we utilize a quasi-variational reformulation of generalized games to show the existence of equilibrium for generalized games in which the constraint maps may admit unbounded values. These existence results are proved by relaxing the convexity assumption on the preferences of players. Finally, we apply the derived results to ensure the existence of equilibrium for the Arrow-Debreu production economy.