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Not really. You don't really decide what the town looks like, you just give them money to fix the place up and when you come back later, the shops are better. I was thinking of Terranigma, where you can't get the best items unless you go around completing quests to upgrade the cities, but the Assassin's Creed series after the first works as well, where you collect rent from your properties and use it to upgrade shops so they carry better items. More like An Investor Is You.
You're playing an otherwise average action-adventure game, and suddenly a town you've saved asks for money, and errands, which they use to fix up the place, changing the aesthetic - and more importantly, upgrade the item shops? It's not a full Simulation Game, it's not even a Mini-Game; you just give them money and stuff, and the town is fixed up while you go about your adventures. What's this mechanic called?