When, In any given society, disparities in wealth and power develop and are perpetuated by rigging the game, we can say that those who can and do rig the game represent an Oligarchy. Oligarchical power can be perpetuated by a group that has disproportionate power by various means, often used in combination. For example, laws of inheritance, civil laws, and religious, natural and supernatural laws are typically employed.

To put this more simply, those who for whatever reason, come to have more power than others, seek to perpetuate their power by rigging the social order in their favor.

I believe that oligarchies could only arise in societies in which excess wealth could arise, and these societies first arose about 5,000 or 10,000 years ago, with the beginning of agricultural technologies that enabled the production of such wealth.

Since disparities in power will always arise in societies that produce excess wealth, those societies can only avoid the problems that come from the formation of oligarchies by setting up rules that break up oligarchies from time to time.

Hope that helps!