in Human evolution, cultural constructs regarding mating are driven by the "cheap sperm, costly eggs" dynamic, tempered by a simple fact...
Women KNOW if a child is theirs.... men can not.
Women are driven by security issues because they can not possibly have as many offspring as a male potentially can... and each of their offspring requires from them a much greater investment in time and resources than the male is required to provide. They need a safe environment in which to raise their offspring... one with food shelter and security.
A man may sire bastards hither and yon without even knowing they were born... he can ensure his genetic legacy thru numbers... whereas a woman can only ensure her genetic legacy by making sure some of her children survive to reproduce.
Because we are self aware, and because we have material legacies as well as genetic ones, in the form of wealth, property, social standing, etc... Men would like to feel that they can have at least some children that they can be assured are theirs to hand down these other benefits...
Because being the child of a chief is a real enhancement to your gene's survival.
A male strategy, then, is to offer the woman the thing she wants, security, in exchange for the thing he wants... assurance that her children are also his children.
This, by the way is what is meant by the term "double standard".
Lots of folks think it means men having it all their way... it doesn't...
The double standard evolved because childbirth is risky as women age. Thru most of human history, childbirth was the leading cause of death in women.
At some point, if a woman wants to ensure HER children inherit the legacy, she must stop having sex with her husband ( in the pre-birth control days) but the man still wants to have sex...
But the worst thing that could happen to a woman, progeny-wise, is to die young... have the husband re-marry, and all the material and social legacy he has accrued be taken by the second wife's children ( the source of the "evil stepmother" image)
The double standard was the tacit negotiation that the wife would turn a blind eye to her husband's dalliances... and in return he would NEVER divorce her. Her future, her children's future, were secured. And he was allowed a hedge, just in case some of the children he was raising were, in fact, not his. (often the case)
Polygyny develops in cultures where wealth is concentrated in the hands of very few, or where life is so hard that acquiring wealth requires a larger number of people than a normal nuclear family.
It is not inherently a stable construct, because women, in more affluent settings, do not have to share social and material legacy with other women's children.
Thus, as women gain the options to provide their own security... or as the average man is better able to offer that security, women naturally demand single pair mating.
If the sheik is super rich... a woman getting one 20th of a kingdom for her children may be far better gamble than even a hard working regular guy could ever offer....
But in a society where woman may be much better off if she can provide her children with her own material legacy that she is assured of... that harem shit won't fly.