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<p>This paper is devoted to the investigation of weak Nash equilibria of set payoffs games (WNESPG in short) with infinitely many players. An existence result of WNESPG is first given by virtue of finite intersection property. Then, the upper and lower semi-continuity of the solution mapping for WNESPG are studied under parameter perturbations of set-valued payoff functions and strategy sets. Moreover, the generalized Hadamard well-posedness of WNESPG with a continuum of players is established. Specifically, when the set-valued payoff function reduces to a scalar-valued one, the generalized well-posedness of Nash equilibria is also given by constructing a bounded rationality function.</p>

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On Nash Equilibria of Set Payoffs Games with Infinitely Many Players

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Yu Zhang,
  • Xiangkai Sun

摘要

This paper is devoted to the investigation of weak Nash equilibria of set payoffs games (WNESPG in short) with infinitely many players. An existence result of WNESPG is first given by virtue of finite intersection property. Then, the upper and lower semi-continuity of the solution mapping for WNESPG are studied under parameter perturbations of set-valued payoff functions and strategy sets. Moreover, the generalized Hadamard well-posedness of WNESPG with a continuum of players is established. Specifically, when the set-valued payoff function reduces to a scalar-valued one, the generalized well-posedness of Nash equilibria is also given by constructing a bounded rationality function.