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Quantifying the likelihood of learning collusive strategy equilibria.

Janusz M Meylahn1

  • 1Department of Applied Mathematics, University of Twente, Enschede, The Netherlands.

Chaos (Woodbury, N.Y.)
|August 1, 2025
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Summary
This summary is machine-generated.

We developed a method to quantify collusive strategies in decentralized multiagent reinforcement learning (MARL) algorithms. This helps assess the societal threat of algorithmic collusion and analyzes Decentralized Q-learning convergence probabilities.

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Area of Science:

  • Artificial Intelligence
  • Game Theory
  • Machine Learning

Background:

  • Decentralized multiagent reinforcement learning (MARL) algorithms are increasingly used in economic settings.
  • Assessing the potential for algorithmic collusion in these systems is crucial for societal impact.
  • Existing methods lack robust quantification of collusion likelihood.

Purpose of the Study:

  • To develop a quantitative method for assessing collusive strategies in provably convergent decentralized MARL algorithms.
  • To analyze the conditions for weak acyclicity in two-player, symmetric Markov games.
  • To evaluate the convergence properties and collusion risks of Decentralized Q-learning.

Main Methods:

  • Introduction of individual best-response graphs for analyzing Markov games.
  • Derivation of conditions for weak acyclicity based on graph properties.
  • Characterization of stationary distributions for strategy adjustment processes.
  • Analysis of Decentralized Q-learning in specific two-player, two-action games.

Main Results:

  • Established conditions for weak acyclicity in relevant Markov games.
  • Demonstrated that individual best-response graphs belong to the class of functional relations.
  • Characterized the stationary distribution of the best-response strategy adjustment process.
  • Showed provable convergence of Decentralized Q-learning in tested scenarios.

Conclusions:

  • The developed method provides a quantitative assessment of algorithmic collusion risks.
  • The findings are applicable to understanding decentralized MARL algorithm behavior in strategic settings.
  • Decentralized Q-learning's convergence and equilibrium selection are better understood in the context of potential collusion.