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The interplay between exploration and exploitation in competitive multi-agentlearning is still far from being well understood. Motivated by this, we studysmooth Q-learning, a prototypical learning model that explicitly captures thebalance between game rewards and exploration costs. We show that Q-learningalways converges to the unique quantal-response equilibrium (QRE), the standardsolution concept for games under bounded rationality, in weighted zero-sumpolymatrix games with heterogeneous learning agents using positive explorationrates. Complementing recent results about convergence in weighted potentialgames, we show that fast convergence of Q-learning in competitive settings isobtained regardless of the number of agents and without any need for parameterfine-tuning. As showcased by our experiments in network zero-sum games, thesetheoretical results provide the necessary guarantees for an algorithmicapproach to the currently open problem of equilibrium selection in competitivemulti-agent settings.

Exploration-Exploitation in Multi-Agent Competition: Convergence with Bounded Rationality