What are the benefits? It depends on woman and as well who she got married to and to great extend other wives.
In some culture, first wife demands that she will select second wife, just to make sure the coming wife is someone she already knew and will not compete with her or ruin her position.
Allah (sw), even though He allowed polygamy, has warned men about it and assure them that it is not easy to be fair. Most muslim men does not enter in to polygamy wholeheartedly, it is usually through an obligation or situation. Of course, I am talking about true men, who take their responsibility seriously, since in Islam, it is upon man to provide for his wives, and thus he get wear out quickly unless he is wealthy and have means and time to support a huge family.
I have seen ugly side of polygamy, where men cheat on their wives and a wife finds out later that she is sharing her husband with another woman. It is heart breaking situation and men usually get off the hook by pointing out that Allah (sw) has granted them permission to have upto 4 wives. In such situation woman felt down by religion and as well by her husband and live a bitter life or very rarely divorce and remarry with someone more honest.
In my view, people do not go in to polygamy seeking benefit but rather as a resort to fullfil their lustful desires (since Islam does not allow adultory), or to help someone in dire situation (either lost husband, less men due to war or feminine) or difficult to say "No" to someone who want to marry him (friend, someone whoem he is in debt of gratitude, or elders who insists), or for noble cause (spread education/spiritual sciences).
The last case I mentioned is interesting. A great saint, I read, did not marry until he was 50. He spend all his youth in studying and meditating. At age 50, after he attend the spiritual station, he married more then one wife, had many children, and educated them. Later among his kids, many saints and learned people came.
