Discordia by IRON Games app for iPhone and iPad

The first cities on the Rhine emerged from Roman outposts protecting the border with Germania. As the governor of one of these cities, your task is to develop it in the best possible way, while also defending it against the Germanic tribes. Empress Agrippina and her son Nero will inspect your actions and honor the most successful governor.

In Discordia, you develop your city by building farms, barracks, defenses, harbors, and markets, and by trading with ships. Use your seamen, soldiers, merchants, and farmers profitably, fulfill decrees, and secure privileges — acting carefully at all times so that your city grows neither too fast nor too slow. Will you have the best-developed city at the end of the fourth year and score many points, or will you manage to impress the empress before then and win the game early?

The App offers you weekly single-user challenges in 3 game modes with varying degrees of randomness, so you can compete with players from all over the world in the highscore lists.
But of course you also can just play for yourself and collec tg various achievements.