On the convergence of logit-response to (strict) Nash equilibria

We show that the logit-response dynamics converges to a subset of (strict) Nash equilibria for any weakly acyclic, N-player normal form game. The result holds independently of whether revision opportunities arise as in asynchronous learning or in other ways, as long as the dynamics is regular. Our analysis generalizes and organizes recent convergence results in the literature. Further, it provides a simple selection criterion, because convergence to strict Nash equilibria obtains even in the presence of non-strict, pure-strategy Nash equilibria.