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Crusader kings II and Europa Universalis IV comes into mind
The Civ series ofcourse

Or the Sierra city building series, if you don't mind a little age and 2D. All of them up to Zeus/Poseidon are on GOG. sadly the last (and IMO, best) of the series, Emperor (the Chinese city builder, not the Dune game) was never released as such. They have 3D sequels (Children of the Nile and Caesar IV), but they are not as good.

Crusader Kings II, Total War series (Medieval recommended)

Age Of Empires?

The Civilization series is all about building and managing empires.

Rise of Nations?

Galactic Civilizations
Masters of the Orion
Star Wars Rebellion

besides the popular games, the guild 2 fits also in "rule over people and make decisions that influence an outcome" , less building...less war...but many management and many many politics

Europa Universalis IV for sure