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<p>This paper examines the global Hölder continuity of solutions to strong vector equilibrium problems, specifically under perturbations in both the objective maps and constraints, without relying on scalarization methods. We first introduce new concepts of relaxed strong quasiconvexity for vector maps and thoroughly explore their mathematical properties and interrelationships. Building on these, we establish novel sufficient conditions for the global Hölder continuity of solution maps, extending prior work in the literature. These theoretical results are then applied to practical models, including the Nash equilibria in non-cooperative games and Wardrop equilibria in transportation networks, where we investigate the structural assumptions necessary to ensure global Hölder continuity.</p>

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Hölder Conditions in Equilibrium Problems: Applications to Strategic and Network Settings

  • 期刊论文

  • 发表日期：

    2025年6月25日

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  • Pham Thanh Duoc,
  • Nguyen Huu Danh

摘要

This paper examines the global Hölder continuity of solutions to strong vector equilibrium problems, specifically under perturbations in both the objective maps and constraints, without relying on scalarization methods. We first introduce new concepts of relaxed strong quasiconvexity for vector maps and thoroughly explore their mathematical properties and interrelationships. Building on these, we establish novel sufficient conditions for the global Hölder continuity of solution maps, extending prior work in the literature. These theoretical results are then applied to practical models, including the Nash equilibria in non-cooperative games and Wardrop equilibria in transportation networks, where we investigate the structural assumptions necessary to ensure global Hölder continuity.