Domination-Avoiding Learning Agents Cannot Collude

2026-05-31

AI Summary

This study investigates the emergence of tacit collusion among learning agents in competitive pricing markets and introduces a class of “collusion-avoiding dominant-strategy” agents. By integrating iterative elimination of strictly dominated strategies, external and internal regret minimization, and multiplicative weights with adaptive learning rates, the work provides the first formal proof that such agents asymptotically avoid selecting strategies eliminated by iterated pure-strategy dominance in repeated games, thereby effectively preventing collusion. The theoretical framework applies to arbitrary games and subsumes several prominent learning algorithms, offering rigorous guarantees against algorithmic collusion in price competition settings.

Abstract

An influential paper of Calvano et al. empirically demonstrated that Q-learning agents spontaneously collude when placed as sellers that compete on prices in a natural market model. More recent results of Fish et al. empirically demonstrated that similar collusion happens with commercial LLMs. We formally prove that such collusion can also happen with external-regret-minimizing agents. We identify a very general class of agents, which we term Domination-Avoiding agents, that provably do not collude in such markets. This class contains all Mean-Based agents and all internal-regret-minimizing agents, as well as others such as Multiplicative-Weight agents with variable learning rate and contextual variants thereof. More generally we show that, in any game, this class of agents is guaranteed to jointly learn to almost never play strategies that are eliminated by repeated elimination of purely dominated strategies.

Problem

• collusion
• learning agents
• domination-avoiding
• regret minimization
• market competition

Innovation

• Domination-Avoiding agents
• no collusion
• regret minimization
• elimination of dominated strategies
• multi-agent learning