Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

Vartika Singh; Philip N. Brown

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arXiv · 2609.11863

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

Vartika Singh·Philip N. Brown

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Abstract

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

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BibTeX RIS

Vartika Singh, Philip N. Brown. 2026-09-10. Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees. https://arxiv.org/abs/2609.11863

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