Abstract illustration of AI algorithms strategizing in a complex game.

Game Theory Breakthrough: Fictitious Play Outperforms Regret Minimization in Multiplayer Scenarios

Avery Sinclair in Tech & Innovation December 2025 • 4 min read.

"New research challenges conventional wisdom, revealing that fictitious play, a simpler algorithm, can lead to better Nash equilibrium approximations in complex multiplayer games."

Navigating the world of multiplayer games, whether in economics, simulations, or even complex AI, requires finding optimal strategies. A Nash equilibrium—where no player benefits from unilaterally changing their strategy—is the gold standard. However, calculating these equilibria in games with more than two players is notoriously difficult.

Traditionally, Counterfactual Regret Minimization (CFR) has been the go-to method for approximating Nash equilibrium strategies, particularly after its success in creating superhuman poker-playing AI. But new research is turning this assumption on its head. A recent study suggests that Fictitious Play (FP), a simpler and older algorithm, can outperform CFR in many multiplayer scenarios.

This discovery could have major implications across fields, offering new insights into how AI agents learn and strategize in complex environments. The research not only challenges existing beliefs but also opens doors for more efficient and effective approaches to game theory.

Why Fictitious Play is Making a Comeback: Challenging the Reign of Regret Minimization

Abstract illustration of AI algorithms strategizing in a complex game.

For years, CFR has been the dominant algorithm for approximating Nash equilibria, especially in complex games. CFR works by iteratively minimizing the regret a player feels for not having chosen a different action in the past. This approach led to groundbreaking AI achievements, such as Libratus and DeepStack, which conquered human professionals in poker.

Fictitious Play, in contrast, is an older and conceptually simpler algorithm. In FP, each player chooses their best response to the historical average of their opponents' strategies. Despite its simplicity, FP has a theoretical drawback: it's not guaranteed to converge to a Nash equilibrium in all games, especially multiplayer and non-zero-sum games.

Simplicity: FP is easier to understand and implement than CFR.
Computational Efficiency: In some cases, FP requires less computational resources.
Empirical Performance: The study demonstrates that FP can achieve better Nash equilibrium approximations in various multiplayer settings.

The new study empirically compared FP and CFR across a range of games with varying numbers of players and strategies. The results were surprising: while CFR performed better in two-player zero-sum games (consistent with previous findings), FP consistently outperformed CFR in multiplayer and general-sum games. This suggests that the theoretical limitations of FP might not be as significant in practice as previously thought.

What This Means for the Future of AI and Game Theory

This research highlights the importance of empirical evaluation in algorithm design. While theoretical guarantees are valuable, they don't always reflect real-world performance. The study suggests that FP, despite its limitations, can be a powerful tool for approximating Nash equilibria in complex multiplayer games. Future research may explore hybrid approaches that combine the strengths of FP and CFR or investigate new algorithms inspired by the principles of Fictitious Play.

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2001.11165,

Title: Empirical Analysis Of Fictitious Play For Nash Equilibrium Computation In Multiplayer Games

Subject: cs.gt cs.ai cs.ma econ.th

Authors: Sam Ganzfried

Published: 29-01-2020

Everything You Need To Know

What is the key difference between Fictitious Play and Counterfactual Regret Minimization?

The primary difference lies in their approaches to finding optimal strategies in games. Counterfactual Regret Minimization (CFR) works by iteratively minimizing the regret a player experiences from not having chosen a different action in the past. In contrast, Fictitious Play (FP) has players choose their best response to the historical average of their opponents' strategies. CFR is more complex, while FP is simpler. This fundamental difference in their methodologies leads to varied performance across different game types and complexities, as demonstrated in the research.

Why has Counterfactual Regret Minimization been the dominant algorithm, and what changed?

Counterfactual Regret Minimization (CFR) was the go-to method due to its success in creating advanced AI, particularly in games like poker, leading to superhuman performance. This success solidified its reputation. However, recent research has challenged this dominance by showing that Fictitious Play (FP), a simpler algorithm, can outperform CFR in multiplayer and general-sum games. This shift suggests the importance of empirical evaluation and that theoretical guarantees do not always translate to optimal real-world performance, especially in complex scenarios.

What are the potential benefits of using Fictitious Play in AI and game theory?

Fictitious Play (FP) offers several potential benefits. Firstly, it is simpler to understand and implement compared to Counterfactual Regret Minimization (CFR). Secondly, it can be more computationally efficient in some cases, requiring fewer resources. Most importantly, FP has shown superior empirical performance in multiplayer and general-sum games, leading to better Nash equilibrium approximations. This implies that FP could enable more efficient and effective AI agents in various complex environments.

What are the implications of using Fictitious Play over Counterfactual Regret Minimization for approximating Nash equilibria?

The implications are significant, especially in the context of multiplayer games. Counterfactual Regret Minimization (CFR) has been the standard, especially after its success in poker. However, Fictitious Play (FP) has shown that it can outperform CFR in approximating Nash equilibria in multiplayer scenarios. This could lead to new AI strategies that are more effective and efficient. FP's success suggests that the theoretical drawbacks of FP, such as non-convergence in certain games, may be less significant in practice than previously believed, especially when compared to CFR in these scenarios.

In what types of games does Fictitious Play excel, and why is this significant?

Fictitious Play (FP) excels in multiplayer and general-sum games, where it has been shown to outperform Counterfactual Regret Minimization (CFR). This is significant because it challenges the existing belief that CFR is always superior. The findings suggest that the simplicity and potentially higher computational efficiency of FP can translate into better approximations of Nash equilibria in complex environments with multiple players. It indicates that, in practice, the historical average of opponents' strategies, as used by FP, can lead to more effective strategic learning than regret minimization, as CFR uses.