It is called oligarchy.
aristocratic
Each city-state, or polis, had its own government. Some city states were monarchies ruled by kings or tyrants. Others were oligarchies ruled by a few powerful men on councils. The city of Athens invented the government of democracy and was ruled by the people for many years.
a government ruled by the wealthy
a monarchy
Aristocrats or Wealthy Home owners
A Plutocracy .
aristocratic
Some names for the form of government ruled by the rich or powerful might include, a plutocracy (rule by the wealthy), an oligarchy (rule by the wealthy, connected, educated, royalty), or maybe an aristocracy (rule by a small class of privileged).
aristocracy
The government was a city-state ruled by the wealthy Medici family.
Ancient Mali was ruled by powerful kings
Genoa wass ruled by a doge with a two year term, selected in an oligarchy of wealthy merchant families. These powerful families were rivals and often fought. *Needs some more info*
Genghis Khan ruled parts of China, Asia, and Europe. He was quite wealthy and powerful.
A secular government.
autocratic government
empire
A matriarchy.