If you look at polygamous cultures (Saudi Arabia, China, ancient Israel), they are not as problematic, mathematically, as everyone seems to think. The key point is that only the richest several percentage points routinely marry multiple women, with the highest status men, like a king or emperor having the most wives or concubines. (This also had the benefit of stabilizing dynasties, as men with multiple wives were more likely to produce a male heir.)

So if 1% of the men are marrying 3% of the women, the net effect of this is that you'll just have a few more men on the bottom social strata lacking wives. If your country goes to war a lot, it might even balance out.

Even in countries today where polygamy technically isn't practiced, it is often more common for a rich man to have a mistress than a poor man. In countries like Malaysia and China, it is semi-expected behavior. There's still some elderly men like Stanley Ho that have multiple wives, since polygamy was only outlawed in 1971.

Fun fact: in China, it was traditionally the role of the first wife to pick out the secondary wife(s) for her husband, though this wasn't always followed. Advice from the time recommended picking someone beautiful but dumb, so that she couldn't challenge your dominance of the household.

Sources: Fertility and Pleasure, Sex at Dawn

This would be a good question for /r/askanthropology. One quick note: Polygyny isn't strictly a historical practice and is actually still quite common.

In short, the Comanche Indians simply took women from other people.

The Comanche Indian's polygamist culture sprung up rather rapidly, as a response to an ever-increasing demand for buffalo hides. In the mid-19th century they were valuable, among other things, as driving belts on early industrial machinery. Since it was very fast for a trained Comanche warrior to kill a buffalo from horseback, yet took about a week to prepare the hide for market, it became necessary to take on additional wives to supplement the labor. Thus the move to polygamy was in many ways an economic decision. Wives weren't simply a symbol of being a rich man; they greatly contributed to the continued wealth of their husband.

To solve the problem of not having enough wives, the Comanche turned to kidnapping women from the plains region and northern Mexico. A significant example was the Parker raid, where a nine year old girl was kidnapped. She would be raised as a Comanche and eventually give birth to the last great Comanche chief, Quanah Parker. by the time she was "rescued" she had gone completely native and never really adjusted to the civilized world again.

Source: Empire of the Summer Moon

Is there any instances of polygamy occurring but in reverse. Multiple men and one women? Or is it mainly notable female leaders having a few lovers?

Not quite OP's question, but seems related enough: Have their been any polygamist groups existing within an explicitly monogamous state, and if so how have states responded throughout history? I'm thinking actual identifiable groups like the Latter Day Saints fundamentalists, rather than just individuals who want to be polyamorous.

In some Australian aboriginal nations it wasn't unheard of (and still isn't) for both men and women to have multiple husbands and wives based on "skin types" and were often arranged by elders to ensure there was a wide enough base for continuous breeding, reducing the necessity to go outside the communities and nations to thin out the blood-line as vast distances and a nomadic nature made this more difficult.

Some information here: http://www.alrc.gov.au/publications/12.%20Aboriginal%20Marriages%20and%20Family%20Structures/marriages-aboriginal-societies-today

for more information see the published papers from early settlers to the central Australia regions at Alice Springs library.