Abstract
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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Ju, Q., Hei, F., Liu, Y., Fang, Z., Luo, Y. (2025). From First-Order to Second-Order Rationality: Advancing Game Convergence with Dynamic Weighted Fictitious Play. In: Hadfi, R., Anthony, P., Sharma, A., Ito, T., Bai, Q. (eds) PRICAI 2024: Trends in Artificial Intelligence. PRICAI 2024. Lecture Notes in Computer Science(), vol 15285. Springer, Singapore. https://doi.org/10.1007/978-981-96-0128-8_20
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DOI: https://doi.org/10.1007/978-981-96-0128-8_20
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