Teaching An Old Dynamics New Tricks: Regularization-free Last-iterate Convergence In Zero-sum Games Via BNN Dynamics
2026 · Tuo Zhang, Leonardo Stella
Abstract
Zero-sum games are a fundamental setting for adversarial training and decision-making in multi-agent learning (MAL). Existing methods often ensure convergence to (approximate) Nash equilibria by introducing a form of regularization. Yet, regularization requires additional hyperparameters, which must be carefully tuned--a challenging task when the payoff structure is known, and considerably harder when the structure is unknown or subject to change. Motivated by this problem, we repurpose a classical model in evolutionary game theory, i.e., the Brown-von Neumann-Nash (BNN) dynamics, by leveraging the intrinsic convergence of this dynamics in zero-sum games without regularization, and provide last-iterate convergence guarantees in noisy normal-form games (NFGs). Importantly, to make this approach more applicable, we develop a novel framework with theoretical guarantees that integrates the BNN dynamics in extensive-form games (EFGs) through counterfactual weighting. Furthermore, we impleme
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