We present two logit-Q learning dynamics combining the classical and independent log-linear learning updates with an on-policy value iteration update for efficient learning in stochastic games. We show that the logit-Q dynamics presented reach (near) efficient equilibrium in stochastic teams. We quantify a bound on the approximation error. We also show the rationality of the logit-Q dynamics against agents following pure stationary strategies and the convergence of the dynamics in stochastic games where the reward functions induce potential games, yet only a single agent controls the state transitions beyond stochastic teams. The key idea is to approximate the dynamics with a fictional scenario where the Q-function estimates are stationary over finite-length epochs only for analysis. We then couple the dynamics in the main and fictional scenarios to show that these two scenarios become more and more similar across epochs due to the vanishing step size.

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