A frequency-aware mean-field model of incremental Boltzmann Q-learning in the Prisoner's Dilemma predicts that apparent stable cooperation is a long metastable transient and that high discount factors induce oscillations via a Neimark-Sacker bifurcation.
Sutton and Andrew G
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Deterministic Model of Incremental Multi-Agent Boltzmann Q-Learning: Transient Cooperation, Metastability, and Oscillations
A frequency-aware mean-field model of incremental Boltzmann Q-learning in the Prisoner's Dilemma predicts that apparent stable cooperation is a long metastable transient and that high discount factors induce oscillations via a Neimark-Sacker bifurcation.