Consider a game with a finite number of players and finite action space. Suppose we consider a sequential iterative game-playing process in which, in each period, players myopically select actions that are a best-response to the actions last chosen by all other players.
Question: suppose that after a certain number of iterations no player wants to change action. Hence, the best-response dynamic has converged to some action profile. Is this action profile necessarily a pure strategy Nash equilibrium?