Which form of government, practiced in certain Greek city-states, describes the system of shared rule by a group of elite, wealthy leaders

Oligarchy-a goverment where decisions are made by a group known as the "elite."

The oligarchy in political science is a form of government in which political power is in the hands of a few people, usually of the same social class. The political writers of ancient Greece used the term to designate the degenerate and negative form of aristocracy (etymologically, government of the best). Strictly speaking, the oligarchy will emerge when the succession of an aristocratic system is perpetuated by blood or mythical transfer, without the ethical and managerial qualities of the best arising on their own merit, this definition very close to that of monarchy and even more so to that of nobility.