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Constructing effective algorithms to converge to Nash Equilibrium (NE) is a important problem in algorithmic game theory. Prior research generally posits that the upper bound on the convergence rate for games is \(O\left( T^{-1/2}\right) \) . This paper introduces a novel perspective, positing that the key to accelerating convergence in game theory is “rationality”. Based on this concept, we propose a Dynamic Weighted Fictitious Play (DW-FP) algorithm. We demonstrate that this algorithm can converge to a NE and exhibits a convergence rate of \(O(T^{-1})\) in experimental evaluations.

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From First-Order to Second-Order Rationality: Advancing Game Convergence with Dynamic Weighted Fictitious Play

  • 会议论文

  • 发表日期：

    2025年

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  • Qi Ju,
  • Falin Hei,
  • Yuxuan Liu,
  • Zhemei Fang,
  • Yunfeng Luo

摘要

Constructing effective algorithms to converge to Nash Equilibrium (NE) is a important problem in algorithmic game theory. Prior research generally posits that the upper bound on the convergence rate for games is \(O\left( T^{-1/2}\right) \) . This paper introduces a novel perspective, positing that the key to accelerating convergence in game theory is “rationality”. Based on this concept, we propose a Dynamic Weighted Fictitious Play (DW-FP) algorithm. We demonstrate that this algorithm can converge to a NE and exhibits a convergence rate of \(O(T^{-1})\) in experimental evaluations.