In the paper, behavior of some dynamic processes in multi-player finite games is considered. The strategy adjustment is based on actions and utility functions with possible noise. The authors describe three classes of learning algorithms and prove finite convergence results to a Nash equilibrium within a given positive probability. In particular, such finite convergence results to a pure Nash equilibrium are proved in weakly acyclic games. This dynamic process is applied to a potential congestion game, where a Nash equilibrium corresponds to a centralized goal minimizer after proper choice of tolls and incentives.