Improvement paths in repeated pure coordination games

We apply the one-sided better reply dynamic and the idea of pure strategy profile improvement path to discounted, infinitely repeated pure coordination games (games with common payoffs). If the stage game is finite, starting from any finite complexity repeated game strategy profile, such improvement paths must exist and must be finite. Furthermore, maximal improvement paths always terminate in pure strategy subgame perfect Nash equilibria of the repeated game. Related to this, we conclude with some observations on infinitely repeated infinite pure coordination games.