Agovernment where the power is shared among a small group of wealthy individuals

I got Oligarchy. you can look it up just to double check though.

Probably the answer you seek is OLIGARCHY

Further explanation:

When you say "small group," then oligarchy is likely the best description.  Oligarchy means "rule by a few."   Based on the description, though, "a small group of wealthy citizens," another term that could have been used would be plutocracy, which means rule by the rich.

people cluster in places that have rich soil, fresh water, and mild climates.

explanation:

polar areas, such as antarctica or the south pole.