Well according to the latest research, the answer is No.
High rates of polygyny* do not lock large proportions of men out of the marriage market.
Good news boys! You can share her around as much as you like.
Can you imagine? The Poindexters from Stanford University reckon it is just fine and dandy if our betters have multiple wives. They say there is no evidence it 'reduces the field' for the rest of us hoi polloi, and in fact these clowns say it will actually strengthen our society.
Wow. With science like this we reckon it won't be long before President Littlehands decides that he wants in on some of this action, and legalises polygyny for himself and the other hucksters in his administration.
Men. You can pick and choose as many as you need!
Yep, some dross straight from the hacks of Stanford University. It seems you can pay the monkeys there and get whatever you want. Gives you a lot of confidence in all their other research, doesn't it.
*Polygamy is the general term for having multiple spouses, while Polygyny is the specific practice of one man marrying multiple women.